Question

The function y = 41 ? 0.95x models the difference (in minutes) between men's and women's finishing times for the boston marathon. the number of years since women first officially ran the race in 1972 is represented by x.

a. does the exponential function represent growth or decay?

b. estimate the difference between finishing times in 1990.

c. predict the difference between finishing times in 2005.

Answer 1

We are given a function:
$y=41* 0.95^{x}$

a. Does the exponential function represent growth or decay?
To find out if this is growth or decay we need to observe number that is connected with x. If number is less than 1 we have decay and if it is greaer than 1 we have growth.
In our case we have number 0.95 which is less than 1 so we have decay.

b. Estimate the difference between finishing times in 1990.
x represents the number of years since 1972.
$x=1990-1972=18$
Now we insert this number into equation to get solution.
$y=41* 0.95^{18} = 16.29$

c. Predict the difference between finishing times in 2005.
$x=2005-1972=33$
$y=41* 0.95^{33} = 7.55$