Question

Exponential Growth/Decay Function

Hint/Tip:

Remember, the basic general exponential function form is: y = Abx In detail, b is written as (1-r) where r is the rate of growth or decay, so our detailed formula is: y = A(1-r)x

Always work with the rate as a decimal number, not as percentage. If the rate is given as percent (%), you will need to divide it by 100 to have the decimal form.

The value of a car is $21,500. It loses 12% of its value every year.

(a) Write a function that represents the value y (in dollars) of the car after x years.

(b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)

Answer 1

(a) Write a function that represents the value and (in dollars) of the car after x years.
For this case what we should do is write the equation of exponential type.
We have then:
y = A (b) ^ x
Substituting the values:
y = 21500 (0.88) ^ x
Answer:
y = 21500 (0.88) ^ x

(b) Use the function to estimate the value of the car after 6 years. (round your answer to the nearest whole number)
We use the function found in part (a) and evaluate for x = 6.
We have then:
y = 21500 (0.88) ^ 6
y = 9985 $
Answer:
the value of the car after 6 years is:
y = 9985 $