Mutual Fund Value Growth

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Lesson Parent: 
Marginal Analysis as an Instantaneous Rate of Change
Problem: 

A mutual fund has determined that the value of its investments over the 40 year period from 1970 to 2010 can be approximated by the function V(t)=0.65t4−12.7t3+74t2+2238t+7300 where t is the number of years from 1970. How fast was the value of the fund growing in 1980, 1990, and in 2000?

Answer: 

$2,508 per year, $10,758 per year, and $42,588 per year for 1980, 1990, and 2000, respectively.

SAMPLE SOLUTION

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Solution: 

We are wanting to determine the change in value per change in time. This is just V′(t). Now we know that V(t) is a polynomial function and that the derivative of a polynomial is known. Therefore,

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Since t is the number of years from 1970 we can find how fast the mutual fund was growing in 1980 by solving<Sign in to see all the formulas>. This gives <Sign in to see all the formulas>. Similarly we can find how fast the investment was growing in 1990 and 2000. Here are the results:

Year t V′(t)
1980 10 $\$2,508\mbox{ per year}<Sign in to see all the formulas>\<Sign in to see all the formulas>
1000 30 $42,588 per year