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3 years ago

6

The function LaTeX: f\left(x\right)=2\cdot4^xf ( x ) = 2 ⋅ 4 xcan be used to represent an exponential growth curve. What is the

multiplicative rate of change of the function?
Group of answer choices

2

4

8

32

1 answer:

nikklg [1K]3 years ago

8 0

Option B: 4 is the multiplicative rate of change of the function

Explanation:

The exponential growth function is $f(x)=2(4)^x$

We need to determine the multiplicative rate of change of the function.

First, let us determine the values of function.

x y

1 8

2 32

3 128

4 512

Since, the multiplicative rate of change of an exponential function is the number by which the next term is increasing or decreasing.

Thus, the multiplicative rate of change of the function is given by

Multiplicative rate of change of the function = $\frac{32}{8} =4$

Multiplicative rate of change of the function = $\frac{128}{32} =4$

Multiplicative rate of change of the function = $\frac{512}{128} =4$

Thus, the multiplicative rate of change of the function is 4

Therefore, Option B is the correct answer.

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$t=\frac{6.5-6.7}{\sqrt{\frac{0.5^2}{100}+\frac{0.7^2}{110}}}}=-2.398$

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Since is a bilateral test the p value would be:

$p_v =2*P(t_{208}$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.

Step-by-step explanation:

Data given and notation

$\bar X_{1}=6.5$ represent the sample mean for Atlanta

$\bar X_{2}=6.7$ represent the sample mean for Chicago

$s_{1}=0.5$ represent the sample deviation for Atlanta

$s_{2}=0.7$ represent the sample standard deviation for Chicago

$n_{1}=100$ sample size for the group Atlanta

$n_{2}=110$ sample size for the group Chicago

t would represent the statistic (variable of interest)

$\alpha=0.01$ significance level provided

Develop the null and alternative hypotheses for this study?

We need to conduct a hypothesis in order to check if the meanfor atlanta is different from the mean of Chicago, the system of hypothesis would be:

Null hypothesis: $\mu_{1}=\mu_{2}$

Alternative hypothesis: $\mu_{1} \neq \mu_{2}$

Since we don't know the population deviations for each group, for this case is better apply a t test to compare means, and the statistic is given by:

$t=\frac{\bar X_{1}-\bar X_{2}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}$ (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the value of the test statistic for this hypothesis testing.

Since we have all the values we can replace in formula (1) like this:

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What is the p-value for this hypothesis test?

The degrees of freedom are given by:

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Since is a bilateral test the p value would be:

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Based on the p-value, what is your conclusion?

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we can reject the null hypothesis, and we have significant differences between the two groups at 5% of significance.

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Vertical Shrink by a factor of 1/2
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