Question

A $7,000 motorcycle depreciates at 10% each year. Which value would represent the base of the exponential function that models this situation?

0.90
0.10
1.10
7,000

Answer 1

The base of the exponential function is 0.90

Explanation:

we know that

The exponential function that models this situation is equal to

`V(x)=P(1-r)^(x)`

where

V is the depreciated value

P is the original value

r is the rate of depreciation in decimal

x is Number of Time Periods

in this problem we have

`P=\$7,000\\r=10\%=0.10`

substitute

`V=7,000(1-0.10)^(x)`

`V=7,000(0.90)^(x)`

therefore

The base of the exponential function is 0.90