Will medal !

baxter is thinking about buying a car for $18,500. the table below shows the projected value of two different cars for three years.

number of years 1 2 3
car 1 (value in dollars) 17,390 16,346.60 15,365.80
car 2 (value in dollars) 17,500 16,500 15,500

part a: what type of function, linear or exponential, can be used to describe the value of each of the cars after a fixed number of years? explain your answer. (2 points)

part b: write one function for each car to describe the value of the car f(x), in dollars, after x years. (4 points)

part c: baxter wants to purchase a car that would have the greatest value in 9 years. will there be any significant difference in the value of either car after 9 years? explain your answer, and show the value of each car after 9 years. (4 points)

answer: a) car 1 : exponential function

car 2 : linear function

b) for car 1, function is,

for car 2, function is,

c) the price of car 2 is 1100.4 (approx) more than the price of car 1 after 9 years.

step-by-step explanation:

a) since the given table, for car 1,

x( number of years)         1               2                 3    

y ( value in dollars)         17390       16346.60       15365.8

while the table for car 2,

x( number of years)         1               2                 3    

y ( value in dollars)         17500       16500       15500

since, for car 1, in first year rate of change in car 1 is -1043.4

and in second year rate of change in car 1 is -980.8

which is not constant for every year.

therefore, if f(x) is a function shows the price of car 1 after x year.

then f(x) can not be linear ⇒ f(x) is exponential.

since, for car 2, the rate of change is

which is constant for every year.

therefore, if f'(x) is a function shows the price of car after x year.

then f'(x) must be linear.

b) let

thus, with of the first table,

a = 18500.00321 ≈ 18500 and b= 0.93999878 ≈ 0.94

thus, the function that shows the price of car 1 after x years,

let f'(x) = ax+b

for, x =1

f'(1) = a + b

but according to the above table f(1) = 17500

thus, a+b = 17500 )

similarly, 2 a + b = 16500 )

by solving equation (1) and (2)

we get, a = - 1000 and b= 18500

thus, the function that shows the price of car 2 after x years,

f(x) = - 1000x + 18500

c) after 9 year the price of car 1,

after 9 year the price of car 2,

thus, the difference between the price of car 1 and 2 after 9 years is,

10600.4038412-9500= 1100.40384123≈ 1100.4

answer: y=4000x+14000

step-by-step explanation: