Question

Riley is training to compete in a marathon, following a training plan recommended by her favorite running podcast. She plans to run 12 miles in her first week of training and will increase her mileage by about 10% each week after. Write an exponential equation in the form y=a(b)x that can model Riley's target mileage per week, y, x weeks after she starts training. Use whole numbers, decimals, or simplified fractions for the values of a and b.

Answer 1

y = 12(1.1)^x

Reason: at x = 0 (the first week) y = 12, and each additional week multiplies mileage by 1 + 10% = 1.1. (Equivalently y = 12(11/10)^x.) If you prefer to have x = 1 represent the first week, use y = 12(1.1)^(x-1).