The amount of cookies at lunch can be represented by an exponential decay equation. If there are 100 cookies at the beginning of lunch and after 15 minutes, there are only 15 left, what is the rate at which students ate the cookies?

Answer: 0.12

Step-by-step explanation:

An exponential decay can be written as:

C (t) = A*r^t

Where A is the initial amount of cookies, A = 100

r is the rate that we are searching.

t is time in minutes, we know that at t = 0m

C (0) = 100*r^0 = 100

so at t = 0m we have 100 cookies.

now, we know that at t = 15m we have.

C (15s) = 100*r^ (15m) = 15

r^15 = 15/100 = 0.15

r = (0.15) ^ (1/15) = 0.88

So the rate at which the cookies decrease is 0.88, and 1 - r = 0.12 is the rate at which the kids eat the cookies (meaning that the students ate 12% of the cookies per minute), so the answer is 0.12