Question

Terrence buys a new car for $20,000. The value of the car depreciates by 15% each year. If f(x) represents the value of the car after x years, which function represents the car’s value? f(x) = 20,000(0.85)x f(x) = 20,000(0.15)x f(x) = 20,000(1.15)x f(x) = 20,000(1.85)x

Answer 1

Answer:

Option A is correct

$f(x) = 20,000 \cdot (0.85)^x$

Step-by-step explanation:

An exponential function is given by:

$f(x) = a(1+r)^x$

where,

f(x) represents the value after x years,

a is the initial value and

r is the rate(in decimal)

As per the statement:

Terrence buys a new car for $20,000.

⇒ a = $ 20,000

It is also given that:

The value of the car depreciates by 15% each year.

⇒r = -0.15

Then, substitute these value we get;

$f(x) = 20,000 \cdot (1-0.15)^x$

⇒$f(x) = 20,000 \cdot (0.85)^x$

Therefore, the function that represents the car's value is, $f(x) = 20,000 \cdot (0.85)^x$

Answer 2

Answer

The function represents the car’s value after x years.

f(x) = 20,000(0.85)x

Reason

As given

Terrence buys a new car for $20,000.

The value of the car depreciates by 15% each year.

15 % is written in the decimal form

$= \frac{15}{100}$

= 0.15

Thus

The decrease in the value of car is represented by = a (1 - r)× t

Where a is the original cost

r is the depreciates rate in decimal form

t is time in years.

Here a = $20000 ,r = 0.15 , t = x years

The value of car after x years = 20,000 (1 -0.15)x

                                                 = 20000(0.85)x

Therefore the the value of the car after x years is represented by  f(x) = 20,000(0.85)x .