SOLUTION: The population P of a city grows exponentially according to the function p(t) = {{{16200(1.06)^t}}}, where t is measured in years. When, to the nearest year, will the population re

Algebra ->  Graphs -> SOLUTION: The population P of a city grows exponentially according to the function p(t) = {{{16200(1.06)^t}}}, where t is measured in years. When, to the nearest year, will the population re      Log On


   

Question 91945: The population P of a city grows exponentially according to the function p(t) = 16200%281.06%29%5Et, where t is measured in years. When, to the nearest year, will the population reach 24,000?
Answer by mathispowerful(115) About Me  (Show Source):
You can put this solution on YOUR website!
16200%281.06%29%5Et

this is a solving equation problem.

set up the equation: 16200%281.06%29%5Et+=+24000
divide 16200 on both sides: 1.06%5Et+=+1.48148148
take logarithm on both sides:
t%2Alog%281.06%29=log%281.48148148%29
so t+=+log%281.48148148%29%2Flog%281.06%29
t+=+0.1707%2F0.0253
=6.745
so it is about 7 years.