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)
(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 $
