   Chapter 6, Problem 65RE

Chapter
Section
Textbook Problem

Membership in Credit Unions The membership in Massachusetts credit unions grew at the rate ofR(t) = −0.0039t2 + 0.0374t − 0.0046 (0 ≤ t ≤ 9)million members year in year t between 1994 (t = 0) and 2003 (t = 9). Find the average rate of growth of membership in Massachusetts credit unions over the period in question.Source: Massachusetts Credit Union League.

To determine
The average rate of growth of membership in Massachusetts credit unions over the period.

Explanation

Given information:

The given membership growing rate between years 1994 and 2003 is

R(t)=0.0039t2+0.0374t+0.0046millionsperyear

The time is t in years and for 1994, t is equal to 0 and for 2003, t is equal to 9.

Formula used:

The formula to calculate the average value of the function f(x) over the interval [a,b] is,

Average value=1baabf(x)dx

Calculation:

Use the above formula to get the average rate of growth over the periods.

The average rate of growth of membership in Massachusetts credit unions over the period R(t) is the function f(x) and the interval [a,b] is the period (in years) [0,9] .

Substitute 0.0039t2+0.0374t+0.0046 million members per year for function, 0 for a and 9 for b in the average formula function to get the average rate of growth over the periods.

Averagerate=19009R(t)dt=19009[0.0039t2+0.0374t+0.0046]dt=19(0.0039t33+0.0374t22+0.0046t)|09=19(0

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