I need help with the below word problem

Question

Country A has a growth rate of 2.4% per year. The population is currently 5,591,000, and the land area of Country A is 13,000,000,000 square yards. Assuming this growth continues and is exponential, how long will there be one person for every square yard of land?

Answer 1

I assume you've seen A=P*e^rt as a model for growth and decay problems.

 

Your function would be A = 5,591,000 e^.024t

 

So if there is a person for every square yard, you need to solve

 

13,000,000,000 = 5,591,000 e^.024t         divide both sides by 5,591,000 to get

2325.165444     = e^.024t                          take the ln of both sides to cancel out the e to get

ln 2325.165444 = .024t

7.751546474    =  .024t                        divide by .024 to get

322.9811031    = t

 

So in a little less than 323 years, the population would grow to 13 billion.

 

Hope this helped.