Question

The value of a mountain bike y (in dollars) can be approximated by the model y = 200(0.65)ᵗ, where t is the number of years since the bike was purchased. Does the model represent exponential growth or exponential decay? What is the annual percent increase or decrease in the value of the bike?

Answer 1

The given model represents exponential decay. The annual percent decrease in the value of the bike is 35%.

Step-by-step explanation:

The given model y = 200(0.65)t represents exponential decay. In exponential decay, the value decreases over time. This indicates that the value of the mountain bike decreases over time. In this case, the value of the mountain bike decreases at a rate of 0.65 for every year since it was purchased.

To find the annual percent decrease, we need to calculate the percentage of the decrease. Since the value decreases by 0.65 every year, the annual percent decrease is 1 - 0.65 = 0.35, or 35% decrease.