Question

A new car is purchased for 17300 dollars. The value of the car depreciates at 9.25% per year. What will the value of the car be, to the nearest cent, after 15 years?

Answer 1

Step-by-step explanation:

Exponential Functions:

y=ab^x

y=ab

x

a=\text{starting value = }17300

a=starting value = 17300

r=\text{rate = }9.25\% = 0.0925

r=rate = 9.25%=0.0925

\text{Exponential Decay:}

Exponential Decay:

b=1-r=1-0.0925=0.9075

b=1−r=1−0.0925=0.9075

\text{Write Exponential Function:}

Write Exponential Function:

y=17300(0.9075)^x

y=17300(0.9075)

x

Put it all together

\text{Plug in time for x:}

Plug in time for x:

y=17300(0.9075)^{15}

y=17300(0.9075)

15

y= 4034.0902389

y=4034.0902389

Evaluate

y\approx 4034.09

y≈4034.09

round

Answer 2

For this case we have an exponential equation of the form:

$y = A (b) ^ x$

Where,

• A: initial value
• b: decrease rate
• x: number of years

Substituting values ​​in the given equation we have:

$y = (173000) (0.9075 ^{15})\\y = 4034.1$

Answer:

The value of the car after 15 days is given by:

$y = 4034.1$