# Hey, I need help on log and continuous growth.

1. Oct 1, 2005

### firstwave

Hey, here is a question I couldn't figure out. I think it's actually really easy, but the wording confuses me.

A recent survey showed that the population, P, of Victoria is growing at an annual rate of 1.1%. Let P0 represent the population on January 1, 2001 and let t represent the time, in years, since this date.

Question:
Express P as a function of t in the form P = P0 a^t

Thanks.

2. Oct 1, 2005

### HallsofIvy

Staff Emeritus
You want P= P0at. Since P and t are variables, the only problem is finding the constants P0 and a. You are told to "Let P0 represent the population on January 1, 2001" and aren't told what that is. If you are not given that as a specific number, and can't look it up the only thing you can do is leave like that: P0.
You are told that "the population, P, of Victoria is growing at an annual rate of 1.1%". Okay, if the the population in 2001 was P0 then the population in 2002 (one year later so t=1) had increased by 1.1%:P(1) was P0+ 1.1% of P0= P0+ 0.011P0= 1.011P0.
Now put that into your equation, P= P0at:
1.011P0= P0a1 and solve for a.
(It's not very hard!)