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

Answer:

The base of the exponential function is 0.90

Step-by-step 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