A new car is purchased for 16200 dollars. The value of the car depreciates at 14.25% per year. What will the value of the car be, to the nearest cent, after 6 years?

6440.5

Exponential Functions:

y=ab^x

y=ab  

x

a=\text{starting value = }16200

a=starting value = 16200

r=\text{rate = }14.25\% = 0.1425

r=rate = 14.25%=0.1425

\text{Exponential Decay:}

Exponential Decay:

b=1-r=1-0.1425=0.8575

b=1−r=1−0.1425=0.8575

\text{Write Exponential Function:}

Write Exponential Function:

y=16200(0.8575)^x

y=16200(0.8575)  

x

Put it all together

\text{Plug in time for x:}

Plug in time for x:

y=16200(0.8575)^{6}

y=16200(0.8575)  

6

y= 6440.5029995

y=6440.5029995

Evaluate

y\approx 6440.5

y≈6440.5