Model Exponential Growth and Decay
Solve.
-An endangered species of fish has a population that is decreasing exponentially $\left( A = A _ { 0 } e ^ { k t } \right)$. The population 9 years ago was 1500 . Today, only 1000 of the fish are alive. Once the population drops below 100 , the situation will be irreversible. When will this happen, according to the model? (Round to the nearest whole year.)
A) 51 years from today
B) 52 years from today
C) 50 years from today
D) 53 years from today

Question

Quizplus · Accepted Answer

To find when the population will drop below 100, we first find the decay constant $ k $ using the equation $ 1000 = 1500 e^{9k} $. Solving for $ k $, we get $ k \approx -0.04055 $. Then, using $ 100 = 1500 e^{kt} $, solve for $ t $ to find $ t \approx 60 $ years from 9 years ago, which is 51 years from today.

Model Exponential Growth and Decay Solve (A=A0ekt)\left( A = A _ { 0 } e ^ { k t } \right)(A=A0​ekt)

Model Exponential Growth and Decay
Solve $\left( A = A _ { 0 } e ^ { k t } \right)$