Power Functions and Logs

Question

There are currently 14 frogs in a (large) pond. The frog population grows exponentially, tripling every 10 days. 

How long will it take (in days) for there to be 190 frogs in the pond?

 

a)Time to 190 frogs _____days?

 

b)Time to 1900 frogs _____days?

 

Answer 1

Let A(t) = number of frogs in t days

 

A(t) = A₀e^kt, where A₀ is the original number of frogs and k is a constant

 

A(t) = 14e^kt

 

A(10) = 42 = 14e^10k

 

             3 = e^10k

 

           ln3 = 10k   k = 0.10986

 

A(t) = 14e^0.10986t

 

a). Find t so that A(t) = 190

 

     190 = 14e^0.10986t

 

     13.57143 = e^0.10986t

 

     ln(13.57143) = 0.10986t      t = ln(13.57143)/0.10986

 

                                               ≈ 23.74 days

 

Part b) can be done in a similar manner