Today, in Brazil, there are 462,966 people in prison. The prison population there has been decreasing at a rate of 1.9% per year for the last 10 years. How many prisoners were there in Brazil 10 years ago?
A) 375,002
B) 560,866
C) 607,562
D) 558,844
E) 383,537

Question

Quizplus · Accepted Answer

To find the number of prisoners 10 years ago, we can use the formula for exponential growth/decay: $P = P_0(1 + r)^t$, where $P$ is the final amount, $P_0$ is the initial amount, $r$ is the rate (as a decimal), and $t$ is the time in years. Rearranging to solve for $P_0$, we get $P_0 = \frac{P}{(1 + r)^t}$. Substituting $P = 462,966$, $r = -0.019$ (since the population is decreasing), and $t = 10$, we find $P_0 = \frac{462,966}{(1 - 0.019)^{10}}$, which calculates to approximately 560,866.

Today, in Brazil, There Are 462,966 People in Prison