Let the population function be P ( t ) = 40 e 0.2 t {\displaystyle P(t)=40e^{0.2t}} . The derivative is
P ′ ( t ) = 0.2 ⋅ 40 e 0.2 t {\displaystyle P'(t)=0.2\cdot 40e^{0.2t}} fish/month = 8 e 0.2 t {\displaystyle =8e^{0.2t}} fish/month.
Therefore the rate that the population is growing in 2 months is
P ′ ( 2 ) = 8 e 0.4 {\displaystyle P'(2)=8e^{0.4}} fish/month.
