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 $V(t)=0.65t^4-12.7t^3+74t^2+2238t+7300$ 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: 

$\$2,508\mbox{ per year}$, $\$10,758\mbox{ per year}$, and $\$42,588\mbox{ per year}$ 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 $\$42,588\mbox{ per year}$