Question

In fashion, clothing can quickly go out of style once it has left the runway. If an outfit (a pair of sweatpants) that costs $1250 loses its value by nearly 21% each month, solve for the number of months that it takes for the sweatpants to only cost $25. Round to the nearest month.

Answer 1

To solve for the number of months it takes for the sweatpants to cost $25, we can use the formula for exponential decay.

Step-by-step explanation:

To solve this problem, we can use the formula for exponential decay:

V = P(1 - r)^t

Where V is the final value, P is the initial value, r is the rate of decay, and t is the time. In this case, we want to find the number of months, so we need to rearrange the formula:

t = log(V/P) / log(1 - r)

Plugging in the values, we get:

t = log(25/1250) / log(1 - 0.21)

Solving this equation gives us t = 13 months.