Question

exponential regression
the table below shows the value, v, of an investment (in dollars) after n years.

n	0	3	7	12	14	19
v	2900	3105.53	3566.63	4258.75	4386.51	4830.91

use your calculator to determine the exponential regression equation that models the set of data above. round the \a\ value to two decimals, and round the \b\ value to three decimals. use the indicated variables.
v =
based on the your regression model, what is the percent increase per year?
%
use the rounded regression model from part 1 to find v when n = 20. round your answer to two decimal places.
v =
interpret your answer by completing the following sentence. be sure to use units in your answer.
\the value of the investment after 20 years is \.
question help: video message instructor

Explanation:

Step1: Use calculator for regression

Most scientific - calculators have an exponential regression function. Input the data points \((n,V)\) where \(n\) is the number of years and \(V\) is the value of the investment. The general form of an exponential regression equation is \(V = ab^{n}\). After using the calculator, we get \(a\approx2900.00\) and \(b\approx1.023\). So the exponential regression equation is \(V = 2900.00\times(1.023)^{n}\).

Step2: Find percent increase

The formula for percent increase in an exponential growth model \(y = ab^{x}\) is \((b - 1)\times100\%\). Since \(b = 1.023\), the percent increase per year is \((1.023-1)\times100\%=2.3\%\).

Step3: Find \(V\) when \(n = 20\)

Substitute \(n = 20\) into the equation \(V = 2900\times(1.023)^{20}\). First, calculate \((1.023)^{20}\approx1.5999\). Then \(V=2900\times1.5999 = 4639.71\).

Answer:

\(V = 2900.00\times(1.023)^{n}\)
\(2.3\%\)
\(V = 4639.71\)
The value of the investment after 20 years is \(\$4639.71\).