story problem

Question

one hundred young trout are put in a fishing pond. three months later the owner estimates that about 65 trout are left. find an exponential formula and then use it to estimate how many trout are in the pond after one year

Answer 1

t = time in months since the 100 fish were put in the pond

 

P(t) = fish population at time t

 

P(t) = P(0)a^t = 100a^t

 

P(3) = 65

 

65 = 100a³

 

a = (65/100)^1/3 ≅ 0.8662

 

P(t) = 100 (0.8662)^t

 

P(12) = 100 (0.8662)¹² ≅ 17.84 ≅ 18