Hey, I on log and continuous growth.

[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.

 

[HallsofIvy]

You want P= P₀a^t. 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= P₀a^t:
1.011P₀= P₀a¹ and solve for a.
(It's not very hard!)