SOLUTION: The population of a town in the year 2000 was 250million and the population growth rate is 0.55% per year. Use the population model P(t)=P0(1+r)^t to find the year when the populat

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The population of a town in the year 2000 was 250million and the population growth rate is 0.55% per year. Use the population model P(t)=P0(1+r)^t to find the year when the populat      Log On


   

Question 867252: The population of a town in the year 2000 was 250million and the population growth rate is 0.55% per year. Use the population model P(t)=P0(1+r)^t to find the year when the population reaches 350million. Answer is 2061
I can't figure out what numbers to plug into what function to solve this. The only example I have of using this formula isn't finding a year so it's not working.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Formulas and recipes are overrated.
0.55% =0.55%2F100=0.0055
The increase in population after the first year is 0.0055%2AP%5B0%5D .
So the population goes from P%5B0%5D to
P%5B0%5D%2B0.0055%2AP%5B0%5D=1.0055%2AP%5B0%5D .
The population increases by the same 1.0055 factor every year.
After t years, the population is
P%28t%29=P%5B0%5D%2A1.0055%5Et .
You need to find the time t years after 2000, when P%28t%29=350million ,
knowing that in 2000, the population is P%5B0%5D=250million
350million=250million%2A1.0055%5Et
350million%2F%22250+million%22+=1.0055%5Et
7%2F5+=1.0055%5Et or 1.4=1.0055%5Et
Taking logarithms on both sides of the equal sign
log%281.4%29=log%281.0055%5Et%29
log%281.4%29=t%2Alog%281.0055%29
t=log%281.4%29%2Flog%281.0055%29
That yields t=61 (rounded to nthe nearest integer.
So the population reaches 350million 61 years after 2000,
in the year 2061.

NOTE:
Since 1.0055=e%5Eln%281.0055%29<-->1.0055%5Et=%28e%5Eln%281.0055%29%29%5Et=e%5E%28t%2Aln%281.0055%29%29 ,
and math teachers really like the irrational number e ,
they often write the function as
P%28t%29=P%5B0%5D%2Ae%5E%28t%2Aln%281.0055%29%29 .
It is really the same thing.