SOLUTION: The formula A = 184e0.038t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 302 thousand?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: The formula A = 184e0.038t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 302 thousand?      Log On


   

Question 1112844: The formula A = 184e0.038t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 302 thousand?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The formula A+=+184%2Ae%5E%280.038t%29 models the population of a particular city, in thousands, t years after 1998.
When will the population of the city reach 302 thousand?
:
184%2Ae%5E%280.038t%29+=+302
divide both sides by 184
e%5E%280.038t%29+=+302%2F184
using natural logs
ln%28e%5E%280.038t%29%29+=+ln%28302%2F184%29
log equiv of exponent
.038t%2Aln%28e%29+=+ln%28302%2F184%29
ln of e is 1
.038t+=+ln%28302%2F184%29
use the calc to find the decimal equiv
.038t = .49549
t = .49549%2F.038
t ~ 13 yrs, 1998 + 13 = 2011