Expert: Paul Klarreich - 11/5/2011

Question
A community grows in such a way that t years from now, its population is P(t) thousand, where
P(t)=51+100ln(t+2)

A) How long does it take for the population to double in initial value?

B) What is the average rate of growth of the population over the first 10 years?

I have the answers but I need help with the steps to get there.  Thanks!
The answers:
A) e^(271/100)-3=12 years
B)ln13/3= 14700 ppl/yr

Answer
Questioner: Kristen
Country: Tennessee, United States
Category: Advanced Math
Private: No
Subject: Logarithmic Functions
Question: A community grows in such a way that t years from now, its population is P(t) thousand, where
P(t)=51+100ln(t+2)

A) How long does it take for the population to double in initial value?

I think that should say:

A) How long does it take for the population to reach double ITS initial value?

1. Determine P(0) = 51 + 100 ln(2)
2. Set P(t) = 2 * that and solve for t.

B) What is the average rate of growth of the population over the first 10 years?

1. Determine P(0) = 51 + 100 ln(2) << oh, yes, we did this already

2. Determine P(10).

3. Avg Rate =

P(10) - P(0)
-------------
 10 - 0

If you need more help, send me what you did and I'll see what I can do.

..........................
I have the answers but I need help with the steps to get there.  Thanks!
The answers:
A) e^(271/100)-3=12 years
B)ln13/3= 14700 ppl/yr