Question

An online movie site offers a 4-year plan that charges $175 for the first year. After the first year, the rates increase by 20% each year. Write an explicit formula that represents the total amount of dollars, an, that a customer would have paid after n years.

A. an = 175(1 + 20)n
B. an = 4.2n + 175
C. an = 175(1.2)n-1
D. an = 1.2(an-1)

Answer 1

The explicit formula that represents the total amount of dollars a customer would have paid after n years is an = 175(1 + 20%)^(n-1).

Step-by-step explanation:

The total amount of dollars a customer would have paid after n years can be represented by the explicit formula an = 175(1 + 20%)^(n-1).

Let's break down the formula:

1. The initial payment is $175 for the first year, so we start with 175.
2. The rates increase by 20% each year, so we multiply the previous year's amount by 1 + 20%.
3. To represent n years, we use the exponent (n-1) after the 1 + 20%.

Therefore, the correct formula that represents the total amount of dollars is an = 175(1 + 20%)^(n-1) (option C).