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Lyrx [107]
3 years ago
8

Vanessa invested $2,500 into an account that will increase in value by 3.5% each year. Write an exponential function to model th

is situation, then find the value of the investment after 20 years.
Mathematics
1 answer:
anygoal [31]3 years ago
5 0

An exponential function is  F = P (1+i)^{t}. $4975 is the value of the investment after 20 years, if Vanessa invested $2500 that will increase in value by 3.5% each year.

Step-by-step explanation:

The given is,

                    Vanessa invested $2,500

                    Increase in value by 3.5% each year

Step:1

             Formula to calculate the future value is,

                                      F = P (1+i)^{t}.............................(1)

           Where, F - Future worth of the investment

                       P - Initial investment

                        i - Rate of increase

                         t - Time taken

        From given values,

                    P = $2500

                     i = 3.5%

                  t = 20 years

       Equation (1) becomes,

                                F = 2500 (1+0.035)^{20}               ( i=\frac{3.5}{100} = 0.035 )

                                    =  2500 (1.035)^{20}

                                    = (2500 × 1.989788)

                                    = 4974.4721

                                    ≅ $4975

                                F = $4975

Result:

             An exponential function is  F = P (1+i)^{t}. $4975 is the value of the investment after 20 years, if Vanessa invested $2500 that will increase in value by 3.5% each year.

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Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that there is significant difference in the time response for the two servers.

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H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0

The significance level is 0.05.

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The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.

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The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that there is significant difference in the time response for the two servers.

<u>Confidence interval </u>

We have to calculate a 95% confidence interval for the difference between means.

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The sample 2, of size n2=225 has a mean of 12.2 and a standard deviation of 4.

The difference between sample means is Md=0.3.

The estimated standard error of the difference is s_Md=0.342.

The critical t-value for a 95% confidence interval and 419 degrees of freedom is t=1.966.

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The 95% confidence interval for the difference in the two servers population expectations is (-0.372, 0.972).

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