this is the 3rd time posting this so the top pictures is the last Wrong one with

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this is the 3rd time posting this so the top pictures is the last Wrong one with the correct answer at the bottom and the bottom picture is the new problem.

This question, with your last answer and correct answer, is displayed below A new car costs $29,000 depreciates to 65 % of its value in 2 years. Round all answers to 2 decimal places, where necessary a. Assume that the depreciation is linear What is the linear function that models the value of this car t years after purchase f(t) Preview syntax error b. Assume that the value of the car is given by an exponential function Aek, where A is the initial price of the car Find the value of the constant k. Answer exactly Preview n 17 to.5/1] c. For the linear model used in part (a), find the value of the car 4 years after the purchase, then do the same for the exponential model used in part (b). Round your answer to 2 decimal places. Linear after 4 years: S Exponential after 4 years: S Answer: 29000 5075t Answer Answer: 8700 Answer: 12252.5 | on In(0.65) 2

Explanation / Answer

cost of new car = $ 29000

depreciates to 65% in 2 years

so we have two points ( 0 , 29000 )

( 2 , 18850 )

a) finding linear function

slope = ( 18850 - 29000 ) ( 2- 0 )

= -5075

hence , linear equation is

29000 - 5075t

b)  finding exponential equation

y = Ae^kt

29000 = A e^k(0)

A = 29000

18850 = 29000 e^(2k)

18850 / 29000 = e^2k

.65 = e^2k

k = ln (.65) / 2

c) value of car 5 years after it was purchase = 29000 - 5075(4)

linear after 4 years = $ 8700

exponential after 4 years = 29000 e^( ln .65/2 ) (4)

exponential after 4 years = $ 12252.5

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