Question

Suppose a new car is worth $30,000. You can use the function y=30,000(0.85)^x to estimate the car’s value after x years. What is the decay factor? What does it mean?

Answer 1

The decay factor here is 0.85, and it means the car’s value changes by 85% every year, or goes down by 15% every year.



The formula for exponential decay is y = a(1 - b)^x

y is the final amount.

a is the initial amount, which is $30,000 in this case.

(1 - b) is the decay factor, or the number the original value gets multiplied by each year, which is 0.85 here.

b is the percent decrease in decimal form. In this case, we can find it using the formula (1 - b) = 0.85. We soon find that b = 0.15, or 15%.

x is the number of years.