Question

Question 2:

You are comparing the price of two different cars. The cost of car A f(x) after x years can be represented by the function:
Car A: f(x) = 22,500(0.88)x
The table shows the cost of car B g(x) after x years:
Car B:
1 year 24,750
2 years 20,495.48
3 years 16,970.26
g(x), cost in dollars




a) Is the cost of Car A increasing or decreasing? How do you know? By what percentage is it changing each year?





b)What is the percent change for Car B?






c)Whose percent change per year is greater, Car A or Car B?

Answer 1

Car A is decreasing in cost, Car B's percent change needs to be calculated, and compare the percent change of both cars.

Step-by-step explanation:

a) The cost of Car A is decreasing because the exponential function f(x) = 22,500(0.88)x has a base less than 1. This means that as x increases, the value of the function decreases. The percentage change each year can be found by subtracting the previous year's cost from the current year's cost, dividing by the previous year's cost, and multiplying by 100.

b) To find the percent change for Car B, we can calculate the percentage difference between the cost after each year. For example, the percent change between year 1 and year 2 is ((20,495.48 - 24,750) / 24,750) * 100.

c) To determine whose percent change per year is greater, compare the percentages calculated in parts a and b.