SOLUTION: 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(n) 2300 2391.96 2641.98 3004.46 3034.8 3183.13 Use yo

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 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(n) 2300 2391.96 2641.98 3004.46 3034.8 3183.13 Use yo      Log On


   

Question 966057: 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(n) 2300 2391.96 2641.98 3004.46 3034.8 3183.13
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 and proper function notation.
V(n) =2308.43(1.019)^n I was able to solve this part of the problem

Based on the your regression model, what is the percent increase per year?
1.9% I was able to solve this part of the problem
Find V(20). Round your answer to two decimal places.
V(20) = I came up with $3,243.61

How long will it take for the value of this investment to reach $11,500? Round your answer to two decimal places.
V(n) = 11500 when n =
I wasn't able to solve this part of the problem
How long will it take for the value of the investment to double? Round your answer to two decimal places.
V(n) has doubled when n =
I wasn't able to solve this part of the problem
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
How long will it take for the value of this investment to reach $11,500? Round your answer to two decimal places.


Use logs to isolate the exponent.


V%28n%29+=2308.43%281.019%29%5En


11500+=2308.43%281.019%29%5En


11500%2F2308.43=%281.019%29%5En


4.9817408368=%281.019%29%5En


%281.019%29%5En+=+4.9817408368


log%28%28%281.019%29%5En%29%29+=+log%28%284.9817408368%29%29


n%2Alog%28%281.019%29%29+=+log%28%284.9817408368%29%29


n+=+log%28%284.9817408368%29%29%2Flog%28%281.019%29%29


n+=+85.31507611


n+=+85.32


It will take roughly 85.32 years

Side note: the reason why it takes so long is because the interest rate is quite dismal. The interest rate of 1.9% is very very small compared to better investments out there.

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I'll let you do the second part. You simply plug in V(n) = 4600 (since 2,300*2 = 4,600) and solve for n using logs. The steps are similar to above because you'll also use logs to isolate n.

If you need help with the second part, then let me know.