SOLUTION: I was wondering if you could perhapse teach me how to solve this question step by step. thank you. Topic: Undoing the exponential If a population is modelled with P = 12,30

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I was wondering if you could perhapse teach me how to solve this question step by step. thank you. Topic: Undoing the exponential If a population is modelled with P = 12,30      Log On


   

Question 26946: I was wondering if you could perhapse teach me how to solve this question step by step. thank you.
Topic: Undoing the exponential
If a population is modelled with P = 12,300 e to the power of 0.073t; t in years
When will the population reach 20,000 people provided it keeps growing in the same fashion. In other words how would we solve this equation step by step please? thank you!
Answer by mbarugel(146) About Me  (Show Source):
You can put this solution on YOUR website!
(Sorry, I accidentally clicked the Post Answer button previously. This is the correct answer)
The population model is:
P=12300e%5E%280.073t%29
SO we have to solve:
20000=12300e%5E%280.073t%29 for t
First divide both sides by 12300
20000%2F12300+=+e%5E%280.073t%29
Then take the natural logarithm of both sides:
ln%2820000%2F12300%29+=+ln%28e%5E%280.073t%29%29
Recall that ln%28e%5Ex%29=x
So we get:
ln%2820000%2F12300%29+=+0.073t
t+=+ln%2820000%2F12300%29%2F0.073
t+=+6.65 years