Question

(04.07 HC)
Summer is thinking about buying a car. 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)
45,000
40,500
36,450
Car 2 (value in dollars)
45,000
42,000
39,000

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: Summer wants to purchase a car that would have the greatest value in 14 years. Will there be any significant difference in the value of either car after 14 years? Explain your answer, and show the value of each car after 14 years. (4 points)

Answer 1

Answer:

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Answer 2

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Account A: Decreasing at 8 % per year

Account B: Decreasing at 10.00 % per year

Step-by-step explanation:

Account B shows the greater percentage change

Part A: Percent change from exponential formula

f(x) = 9628(0.92)ˣ

The general formula for an exponential function is

y = ab^x, where

b = the base of the exponential function.

if b < 1, we have an exponential decay function.

ƒ(x) decreases as x increases.

Account A is decreasing each year.

We can rewrite the formula for an exponential decay function as:

y = a(1 – b)ˣ, where

1 – b = the decay factor

b = the percent change in decimal form

If we compare the two formulas, we find

0.92 = 1 - b

b = 1 - 0.92 = 0.08 = 8 %

The account is decreasing at an annual rate of 8 %.The account is decreasing at an annual rate of 10.00 %.

Account B recorded a greater percentage change in the amount of money over the previous year.