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

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.