Question

The following function represents the value of a car, in dollars, after x years:

f(x) = 24,000(0.92)power of x

What does 0.92 represent?

A.The present value of the car

B.The value of the car after x years

C.The decrease in the value of the car, which is 92%

D.The decrease in the value of the car, which is 8%​

Answer 1

D.The decrease in the value of the car, which is 8%​

Explanation:

Since, in the exponential function,

`f(x)=ab^x`

a is the initial value,

b is the growth ( if > 1 ) or decay factor ( if between 0 and 1 ),

Here, the given equation that shows the value of car after x years,

`f(x)=24000(0.92)^x`

By comparing,

b = 0.92 < 1

Thus, 0.92 is the decay factor that shows the decrease in the value of car,

∵ Decay rate = 1 - decay factor

= 1 - 0.92

= 0.08

= 8%

Hence, the value of car is decreasing with the rate of 8%.

Option 'D' is correct.

Answer 2

Option D.The decrease in the value of the car, which is 8%

Explanation:

we have a exponential function of the form

`f(x)=a(b)^(x)`

where

y is the value of the car

x is the time in years

a is the initial value

b is the base

r is the rate of decrease

b=1+r

In this problem we have

a=$24,000 initial value of the car

b=0.92

so

0.92=1+r

r=0.92-1=-0.08=-8%-----> is negative because is a rate of decrease