The population of a certain city was 135000 in 1998, and the observed relative growth rate is 2 percent per year.
a.)Find a function that models the population after t years, compounded continuously.

b.) Find the projected population in the year 2004.

c.) In what year will the population reach 182230?

So i was able to work out the problems and get the correct answers for a and c, but I cannot seem to figure out how to get b. do i need to use the formula: A=P(1+r/n)^(nt) ? I'm not sure where to go with b.

Question

The population of a certain city was 135000 in 1998, and the observed relative growth rate is 2 percent per year.
a.)Find a function that models the population after t years, compounded continuously.

b.) Find the projected population in the year 2004.

c.) In what year will the population reach 182230?

So i was able to work out the problems and get the correct answers for a and c, but I cannot seem to figure out how to get b.   do i need to use the formula: A=P(1+r/n)^(nt) ? I'm not sure where to go with b.

anonymous · Answer

Exponential growth function is of the form.$$P(t)=P_0e^{rt}$$Insert the givens from the problem to get$$P(t)=135,000e^{.02t}$$

anonymous · Answer

The formula you referred to is for periodically compounded interest, not continuously.

anonymous · Answer

Once you have the function above, parts b and c follow pretty easily.

anonymous · Answer

thank you very much!

anonymous · Answer

No sweat.  Do math every day.

anonymous · Answer

okay I have a question. I have the function and found the answer to a and c just fine. I'm having a hard time with b: it's asking for the projected population in 2004. for my t, do i make that 2004?

anonymous · Answer

The model starts in 1999, so t is the number of years after 1998; for 2004 it will be six.