Differentiate. . g(x) = log 47(2x - 4) g'(x) = Differentiate. 8 y= log2 (x® + x) d | log2 (x® + x) = 0 = dx Differentiate. 6 9(x) = x (7.5)* g'(x) = The population of Nilam doubles in size every 6 yr. In 1989, its population was 20,000. t т a) Find an exponential function of the form P(t)= Pon' that models Nilam's population after t years. b) Find the equivalent exponential model of the form P(t) = Poen. c) What is Nilam's yearly percentage growth rate? d) Without using a calculator, find Nilam's population in 2007. e) How fast was Nilam's population changing in 1999? t T a) Find an exponential function of the form P(t) = Pon' that models the situation. = = The exponential function is P(t) = (Use integers or fractions for any numbers in the expression.)

Answers

Answer 1

After differentiation, g'(x) = ln(47)/(x - 2)

a) P(t) = P(0) * \(2^{(t/6)\)

b) P(t) = 20,000 * \(e^{(ln(2)t/6)\)

c) r ≈ 11.56%

d) Nilam's population in 2007 was 160,000.

e) Nilam's population was changing at a rate of approximately 18,198.9 people per year in 1999.

Differentiation:

g(x) = log47(2x - 4)

g'(x) = ln(47)/(2x - 4)(2x - 4)

g'(x) = ln(47)/(2x - 4)

g'(x) = ln(47)/(x - 2)

y = log2(x² + x)

d/dx [log2(x² + x)] = 1/(ln2) * (d/dx)(x² + x) * 1/(x² + x)

Using the chain rule, (d/dx)(x² + x) = 2x + 1

d/dx [log2(x² + x)] = 1/(ln2) * (2x + 1)/(x² + x)

g(x) = 9x(7.5)

g'(x) = 9(7.5)

a) Let P(t) be the population of Nilam after t years. Given that the population doubles every 6 years, we have:

P(t) = P(0) * \(2^{(t/6)\)

where P(0) is the initial population (in 1989) which is 20,000.

b) We can rewrite P(t) as:

P(t) = 20,000 * \(e^{(ln(2)t/6)\)

which is of the form P(t) = Poen, where Po = 20,000 and n = ln(2)/6.

c) The yearly percentage growth rate r is given by:

r = 100 * \((2^{(1/6)} - 1)\)

Using a calculator, we get:

r ≈ 11.56%

d) To find the population of Nilam in 2007 (18 years after 1989), we plug t = 18 into the exponential function we obtained in part a):

P(18) = 20,000 * \(2^{(18/6)\)

P(18) = 20,000 * \(2^3\)

P(18) = 160,000

Therefore, Nilam's population in 2007 was 160,000.

e) To find how fast Nilam's population was changing in 1999 (10 years after 1989), we take the derivative of the exponential function we obtained in part a) with respect to t:

P'(t) = (ln2/6) * 20,000 * \(2^{(t/6)\)

Then we plug t = 10 into the derivative to get:

P'(10) = (ln2/6) * 20,000 * \(2^{(10/6)\)

P'(10) ≈ 18,198.9

Therefore, Nilam's population was changing at a rate of approximately 18,198.9 people per year in 1999.

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Related Questions

What is the measure of this line?

84 mm
80 mm
80.4 mm
840 mm

What is the measure of this line?84 mm80 mm80.4 mm840 mm

Answers

Answer:

84 mm

Step-by-step explanation:

1 cm = 10 mm

8.4 cm = 84 mm

Answer:

the measure of this line is 80.4

What 1-3+9 answe pleaseeeeeee

Answers

That answer will be 7.
Explanation:
=1-3+9
=10-3
=7

Answer:

the answer is 7

Step-by-step explanation:

Question 11.
Brainliest + thanks + 5 stars

Question 11. Brainliest + thanks + 5 stars

Answers

300-275 = 25

25/300 × 100%

= 25/3 %

= 8.3 % (approx.)

brainliest plz

109%
End result / total
300 / 275 = 1.09
Move the decimal to the right twice to get a percentage
=109 %

Does -7 • [-8] = 7• 8

Answers

Hey there!

Guide:

• Negative & negative = positive

• Positive & positive = positive

• Negative & positive = negative

• Positive & negative = negative

~~~~~~~~~~~~~~~~~~~~~~~~~~~

• Positives are above 0

• Negatives are below 0

~~~~~~~~~~~~~~~~~~~~~~~~~~~

• Negatives are on the left side of the number line

• Positives are on the right side of the number

~~~~~~~~~~~~~~~~~~~~~~~~~~~

Answering your question

-7 * -8 = 7 * 8

-7 * -8 = 56

7 * 8 = 56

56 = 56

Answer: YES they are equivalent/equal to each other because both of them equal positive 56.

• It wouldn’t be equivalent if one is a negative number and the other one is positive (even when it looks like the same number). If both numbers are positives / negatives with the same number then they’ll most likely be equivalent/equal to each other!

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

yea, a negative times a negative equals a positive

Which relation is also a function URGENT pls help BRAINLIEST!!!!!!!

Which relation is also a function URGENT pls help BRAINLIEST!!!!!!!

Answers

Answer:

b

Step-by-step explanation:

a chemist is using 356 milliliters of a solution of acid and water. if 19.3% of the solution is acid, how many milliliters of acid are there? round your answer to the nearest tenth.

Answers

The solution contains 68.7 milliliters of acid, according to the data provided.

What is a acid in a solution?

An acid is any substance that tastes sour in water, turns blue litmus paper red, combines with some metals to free hydrogen, reacts without bases to form salts, and facilitates chemical reactions (acid catalysis).

How do you recognize an acid?

Count the hydrogens in each component both before and after the reaction to determine if it is an acid or a basic. If the amount of hydrogens has reduced, that material seems to be the acid (which donates hydrogen ions).

According to the given data:

Solution = 356 milliliters

Acid = 19.3% of solution

The amount of acid in the solution is calculated as:

Acid = 19.3% × 356 milliliters

Evaluate

Acid = 68.708 milliliters

Acid = 68.7 milliliters

The solution contains 68.7 milliliters of acid, according to the data provided.

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1. Let the sample space represent all the values from 1 to 10. Let A = {1, 2, 8} and B = {2, 7}. What is the P(A ∩ B)?

Answers

Answer:

It's {2} since it's the common between A and B

At a school carnival, 3 out of 25 tickets sold were early-admission tickets. What percentage of the tickets were early-admission tickets?

Answers

Answer: 12%

Step-by-step explanation:

Since we are given the information that at a school carnival, that 3 out of 25 tickets sold were early-admission tickets, to calculate the percentage of the tickets that were early-admission tickets goes thus:

= Number of early admission tickets / Total number of tickets × 100

= 3/25 × 100

= 12%

Therefore, the percentage of the tickets were early-admission tickets is 12%.

what are mean squared error formula?

Answers

The mean squared error formula is:

\(MSE=\frac{\sum (y_i-\bar{y})^2}{n}\)

where, MSE is the mean squared error

\(y_i\) - observed values

\(\bar{y}\) - the predicted values

n - the number of data points

We know that in statistics the mean squared error tells us that whether or not a regression line is an accurate model for predicting data points in a particular set of data.

If the mean squared error value is minimum then it indicates an accurate regression model, or, goodness of fit.

The mean square error is calculated by taking the average of errors squared from data.

The formula for the mean squared error is:

\(MSE=\frac{\sum (y_i-\bar{y})^2}{n}\)

where, MSE is the mean squared error

\(y_i\) represents observed values

\(\bar{y}\) represents the predicted values

n represents the number of data points

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can someone help with question b? :)

can someone help with question b? :)

Answers

Answer:

x = 13

Step-by-step explanation:

Substitute for y

y = 5x - 15

50 = 5x - 15

65 = 5x

x = 13


I hope this helped and please mark me as brainliest!

\(\longmapsto\sqrt{64}\)

Answers

\( \sqrt{64} = 2 \times 2 \times 2 \times 2 \times 2 \times 2\)

\( \sqrt{64} = 2 \times 2 \times 2\)

\( \sqrt{64} = 8\)

# Answered by Cutest Ghost..
[tex]\longmapsto\sqrt{64}[/tex]

a television program director has 14 shows available for monday night but can choose only 5 shows. how many different possible combinations are there?

Answers

There are 240240 possible permutations of choosing 5 shows from 14 available shows. It can be obtained by applying the formula of permutation.

What is permutation?

In mathematics, it is the number of ways in which given number of items can be arranged in different orders.

Here, we need to select 5 iteams from the given 14 iteams.

\(P(14,5)=\frac{14!}{(14-5)!}\\=\frac{14!}{(9!)}\\=\frac{(14)(13)(12)(11)(10)(9!)}{(9!)}\\=(14)(13)(12)(11)(10)\\=240240\)

Hence, there are 240240 possible permutations of choosing 5 shows from 14 available shows.

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It takes 0.250.25 cup of sugar to make a batch of chocolate chip cookies. I have 5.505.50 cups of sugar. How many batches of cookies can I make? I can make batches of chocolate chip cookies. You may use the scratchpad to show your work. (b) Lemon Cookies It takes 0.750.75 cups of sugar to make a batch of lemon cookies. I have 5.55.5 cups of sugar. How many batches can I make? I can make batches of lemon cookies. You may use the scratchpad to show your work.

Answers

Answer:

a) 22 batches

c) 7.3 batches

Step-by-step explanation:

a) It takes 0.25 cup of sugar to make a batch of chocolate chip cookies. I have 5.50 cups of sugar. How many batches of cookies can I make?

0.25 cup = 1 batch

5.5 cup = x

Cross Multiply

0.25 cup × x = 5.5 cup × 1 batch

x = 5.5 cup × 1 batch/0.25 cup

x = 22

I can make 22 batches of chocolate chip cookies. You may use the scratchpad to show your work.

(b) Lemon Cookies It takes 0.75 cups of sugar to make a batch of lemon cookies. I have 5.5 cups of sugar. How many batches can I make?

0.75 cup = 1 batch

5.5 cup = x

Cross Multiply

0.75 cup × x = 5.5 cup × 1 batch

x = 5.5 cup × 1 batch/0.75 cup

x = 7.3 batches

I can make 7.3 batches of lemon cookies. You may use the scratchpad to show your work.

what is m if 9/7m= 1/7

Answers

9/7m=1/7
M=1/7*7/9=1/9

Answer: \(m=\frac{1}{9}\)

Step-by-step explanation:

\(\frac{9}{7}m=\frac{1}{7}\)

Multiply by the reciprocal to isolate m.

\((\frac{7}{9} )\frac{9}{7}m=\frac{1}{7}(\frac{7}{9} )\)

\(m=\frac{1}{9}\)

For each diagram, decide if y is an increase or a decrease relative to x. Then determine the percent increase or decrease.(sry the stuff on the pic is black)

For each diagram, decide if y is an increase or a decrease relative to x. Then determine the percent

Answers

Answer:

In A: y is a 25% decrease of x

In B: y is a 25% increase of x

Step-by-sep explanation:

For A:

The diagram in A shows that x = 4, while y = 3.

Thus, this means that y decreased by 1, relative to x.

The percentage decease would be:

\( \frac{1}{4} \times 100 \)

\( \frac{100}{4} = 25 \)

Therefore, y is a 25% decrease of x.

For B:

The diagram for B shows that x = 4, while y = 5.

Thus, this means that y increased by 1, relative to x.

The percentage increase would be:

\( \frac{1}{4} \times 100 \)

\( \frac{100}{4} = 25 \)

Therefore, y is a 25% increase of x.

For each diagram, decide if y is an increase or a decrease relative to x. Then determine the percent

Answer:

Step-by-step explanation:

A- Y is a decrease.

1/4 x 100 = 100/4 =25%

25% and decrease.

B- Y is a increase

1/4 x 100 = 100/4=25%

25% and increase.

I need help with this

I need help with this

Answers

Answer:

10 units²

Step-by-step explanation:

In the second photo.

I need help with this
I need help with this

Mr. Ondonez gives his math students 34 quizzes during 17 weeks of school if he gave the same number because it each week how many quizzes does Mr.Ondonez give his students every week

Answers

Answer:

2 quiz

Step-by-step explanation:

Mr Ondonez gives his students 34 quizzes over 17 weeks. They are given the same number of quiz per week. To calculate the number of quiz given per week, we have to divide the total number of quiz given by the total number of weeks. Therefore:

Number of quiz per week = Total number of quiz / Total number of weeks  

Number of quiz per week = 34 / 17 = 2

The students are given 2 quizzes per week.

Answer:

2 quiz

Step-by-step explanation:

how many nonnegative integers can be written of the form a7 * 3^7 a2 * 3^6 where ai {1, 0, -1} amc

Answers

The non negative integers can be written of the form is 3281.

Given:

a7 * 3^7 a2 * 3^6 where ai {1, 0, -1}.

ai = 7,6,5,4,3,2,1,0

Total = 8

= \(3^{8}\) = 6561

= 6561 - 1 /2

= 6560/2

= 3280 is negative integers

Non negative or positive integers = 6561 - 3280 = 3281

Therefore the non negative integers can be written of the form is 3281.

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What is the value of 7 in 46.897

Answers

Answer:

If your asking its place value its Thousandths

Step-by-step explanation:

.1 is tenths

.01 is hundredths

.001 is thousandths

How do you write 9.085 x 10-9 in standard form?

Answers

Answer: 0.000000009085

Step-by-step explanation: This expression is rewritten like this because it is multiplied by a negative power of ten. Therefore, applying this principle to scientific notation, the answer would have to be less than 0. That would be your answer. Hope this helps!

which of the following is not influenced by stream velocity? discharge suspended load dissolved load abrasion bed load

Answers

The stream velocity has no influence on the amount of dissolved load it contains. The amount of dissolved material depends on erosion and deposition carried out in the watercourse. These are affected by factors such as the slope of the land, the resistance of the material to erosion, the size of the sediments transported, etc.

Which of the following is not influenced by stream velocity?

Dissolved load

Stream velocity plays an important role in the transport of sediments and dissolved loads in a watercourse. It affects the erosion and deposition processes that occur in the watercourse, which in turn affect the amount of sediment and dissolved load that is carried by the stream. For example, faster stream velocities can cause more erosion of the stream bed, leading to more material being carried in the water.

Sediment is any particulate matter that is transported by a fluid, and it can come in many different forms. The three main types of sediment are:

The suspended load is made up of small particles that are carried along in the water column. The bed load consists of larger particles that are moved along the bottom of the streambed. And the dissolved load is made up of particles that are carried in solution.

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What is the surface area of a cube that has a radius of 9 ft and height of 3 ft

Answers

Answer:

If it has a radius of 9 then the length will be 18 and it would be a 18 by 3 shape and that's not a cube....

Step-by-step explanation:

I need help on this question

I need help on this question

Answers

Answer: yes

Step-by-step explanation:

x=5

Answer: Yes, 5 is a substitute for x.

Step-by-step explanation:

Yes, 5 is a substitute for x because, 4x or, 4x5 is 20. Knowing the PEMDAS method, that is what we would use. So since multiplication is first, we use the 4x first.

The other side: 8x or, 8x5, is 40. 40-13=27. So yes, 5 is a substitute for x.

Use both the addition and multiplication properties of inequality to solve the inequality. Graph the solutions on a number line. 2(5y-6)>-2

Answers

Answer:

5+8x

Step-by-step explanation:

I did the math.

i can spell.................................................................

i can spell.................................................................

Answers

Answer:

A

Step-by-step explanation:

What would be the values of the measures of variation if the tuna sushi contained no mercury? A. The measures of variation would all be 0 . B. The measures of variation would all be 1 . C. The measures of variation would all be 0.378. D. The measures of variation would all be undefined.

Answers

A, the measures of variation would all be 0. This is because variation measures the differences or spread of values within a dataset. If there is no mercury present in the tuna sushi, then all the values would be the same, resulting in no variation and all measures of variation would be 0.

that since there is no difference or spread in the data, it is not possible to calculate the range, variance, or standard deviation, which are the measures of variation. Therefore, the correct answer is option A.

In conclusion, if the tuna sushi contained no mercury, the measures of variation would all be 0, as there would be no variation in the data.

The measures of variation describe the dispersion or spread of a dataset. If the tuna sushi contained no mercury, that means there is no variation in mercury content. In this case, all data points would be the same (0 mercury), resulting in no dispersion or spread.

If tuna sushi had no mercury content, the measures of variation would be 0, indicating no dispersion in the data.

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When graphing any equation what is a great fall back plan if you can't remember the learned procedure? (on all kinds of equations - some with x squared, x cubed etc)

Answers

Answer:

Step-by-step explanation:

Arbitrarily choose a couple of x value using the given function, and write your results in  a x-y table as (x, y).  Plot these points.  Connect them with a smooth curve.  if you have any doubts about the shape of the grqph, pick more x values in the neighborhood and plot them also.

Help fast I can’t figure this out

Help fast I cant figure this out

Answers

Answer:

100

Step-by-step explanation:

x^3 = 1,000,000  Find the cube root of 1,000,000

x^3 = 1.0x10^6     Using scientific notation, we can split the 1,000,000 into a 1.0 and a factor of 10*10*10*10*10*10 or 10^6

x = 1.0x10^2         The cube root of 1.0 is 1.0.  The cube root of 10^6 is found by dividing the exponent by 3:  10^2

The cube root of 1,000,000 is 1.0X10^2, or 100.

x = 100

PLEASE HEPPPPPP MEEEEEE :))))

PLEASE HEPPPPPP MEEEEEE :))))

Answers

1)

⇒ x² - 6x = -8

\(\sf add \ 9 \ on \ both \ sides\)

⇒ x² - 6x + 9 = -8 + 9

\(\sf simplify \ and \ complete \ square\)

⇒ x² - 3x - 3x + 9 = 1

\(\sf factor \ common \ term\)

⇒ x(x - 3) - 3(x - 3) = 1

\(\sf collect \ into \ groups\)

⇒ (x - 3)² = 1

\(\sf square \ root \ both \ sides\)

⇒ x - 3 = ±√1

\(\sf simplify\)

⇒ x - 3 = ±1

\(\sf change \ side\)

⇒ x = 1 + 3, -1 + 3

\(\sf simplify\)

⇒ x = 4, 2

2)

\(\rightarrow \sf 4x^2 + 12x + 11 = 0\)

\(\rightarrow \sf 4\left(x^2+3x+\dfrac{11}{4}\right) = 0\)

\(\rightarrow \sf 4\left(x^2+3x+\dfrac{11}{4}+\left(\dfrac{3}{2}\right)^2-\left(\dfrac{3}{2}\right)^2\right) = 0\)

\(\rightarrow \sf 4\left(x+\dfrac{3}{2}\right)^2+2 = 0\)

\(\rightarrow \sf \left(x+\dfrac{3}{2}\right)^2 = -\dfrac{2}{4}\)

\(\rightarrow \sf \left(x+\dfrac{3}{2}\right)^2 = -\dfrac{1}{2}\)

\(\rightarrow \sf x+\dfrac{3}{2} = \pm \sqrt{-\dfrac{1}{2} }\)

\(\rightarrow \sf x+\dfrac{3}{2} = \pm i\sqrt{\dfrac{1}{2} }\)

\(\rightarrow \sf x= \pm i\sqrt{\dfrac{1}{2} }-\dfrac{3}{2}\)

Please 0,45 = ........ % 0,3 = ......... % 1,9 = ........... % 0,01 = ...........% 1 = ............%

Answers

Answer:

45%, 30%, 190%, 1%, 100%

Step-by-step explanation:

To get a percent from a decimal, multiply it by 100 and add a % symbol.

Please 0,45 = ........ % 0,3 = ......... % 1,9 = ........... % 0,01 = ...........% 1 = ............%
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