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2 years ago

The table represents an exponential function

Mathematics

1 answer:

Vedmedyk [2.9K]2 years ago

5 0

The multiplicative rate is 9 if the table that shows an exponential function option fourth is correct.

<h3>What is an exponential function?</h3>

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1

We have a table that shows an exponential function.

As we know the exponential function:

y = a(b)ˣ

Plug x = 1, y = 6

6 = ab ...1

Plug x = 2, y = 4

4 = ab² ...2

Divide equations 1 and 2

ab²/ab = 4/6

b = 2/3

Plug the value of b in the 1 equation.

a(2/3) = 6

a = 9

y = 9(2/3)×

The multiplicative rate = 9

Thus, the multiplicative rate is 9 if the table that shows an exponential function option fourth is correct.

Learn more about the exponential function here:

brainly.com/question/11487261

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a) A sample size of 5615 is needed.

b) 0.012

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

99.5% confidence level

So $\alpha = 0.005$ , z is the value of Z that has a pvalue of $1 - \frac{0.005}{2} = 0.9975$ , so $Z = 2.81$ .

(a) Past studies suggest that this proportion will be about 0.2. Find the sample size needed if the margin of the error of the confidence interval is to be about 0.015.

This is n for which M = 0.015.

We have that $\pi = 0.2$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.015 = 2.81\sqrt{\frac{0.2*0.8}{n}}$

$0.015\sqrt{n} = 2.81\sqrt{0.2*0.8}$

$\sqrt{n} = \frac{2.81\sqrt{0.2*0.8}}{0.015}$

$(\sqrt{n})^{2} = (\frac{2.81\sqrt{0.2*0.8}}{0.015})^{2}$

$n = 5615$

A sample size of 5615 is needed.

(b) Using the sample size above, when the sample is actually contacted, 12% of the sample say they are not satisfied. What is the margin of the error of the confidence interval?

Now $\pi = 0.12, n = 5615$ .