If the population of Dodge City is decreasing at a rate of 19% per year, how long will it take to decrease from 7,700 to 2,000?
A) 7.75 years
B) 6.4 years
C) 9.6 years
D) 5.8 years
E) 4.9 years

Question

Quizplus · Accepted Answer

The population decrease can be modeled by the exponential decay formula $P = P_0(1 - r)^t$, where $P$ is the final population, $P_0$ is the initial population, $r$ is the rate of decrease (as a decimal), and $t$ is the time in years. Plugging in the given values, $2000 = 7700(1 - 0.19)^t$. Solving for $t$ gives approximately 7.75 years.

If the Population of Dodge City Is Decreasing at a Rate