Gas prices are expected to rise 5% each week for the next six weeks. Kevin spent $52.50 to fill his tank this week. Which of the following represents the total amount Kevin can expect to spend to fill his tank over the next three weeks, if he fills his tank once a week?

$52.50 + $55.13 + $57.76

$52.50 + $55.13 + $57.88

$55.13 + $57.76 + $60.39

$55.13 + $57.88 + $60.78

Hello!

To calculate the 5% increase in gas money each week, we can create an exponential equation to determine how much the cost of gas money will increase.

5% of 100 is written as 5/100, or 0.05. With that, we can create our exponential growth function.

f (x) = 52.50 (1 + 0.05) ^x

f (x) = 52.50 (1.05) ^x

With that equation, we can solve for how much the gas prices had increase for the next three weeks. In this equation, x represents the amount of weeks, and f (x) represents the gas price.

Week 1: f (1) = 52.50 (1.05) ^1

52.50 (1.05) = 55.125 | This can be rounded to 55.13 dollars.

Week 2: f (2) = 52.50 (1.05) ^2

52.50 (1.1025) = 57.88125 | This can be rounded to 57.88 dollars.

Week 3: f (3) = 52.50 (1.05) ^3

52.50 (1.157625) = 60.7753125 | This can be rounded to 60.78 dollars.

With those values, Kevin will expect to spend $55.13 + $57.88 + $60.78, which is choice D.