Word problem

Question

The formula A=18e ^0.0055t 

models the pooulation of New York state, A , in millions , t years after 2,000. When will the population reach 24 million ? 

 

 

Answer 1

Set A equal to 24 (million).  Now we have 

 

18e^0.0055t = 24

 

Divide by 18.

 

e^0.0055t = 24/18

 

Now take the natural log of both sides.

 

0.0055t = ln(24/18)

 

Finally, divide by 0.0055.

 

t = ln(24/18) / 0.0055

 

This is approximately 52.3.  Thus in 2052, the population will reach 24 million, according to the model.  

 

Regards,

 

Jake Mirra