Algebra 2 help? Please?

Question

Use a growth or decay model to solve the problem.

A new school district is experiencing an annual growth rate of 9.5%. The school population is now 5600 students. What is the approximate predictied population 10 years from now?

I'd use A=p(1+r/n)^nt, right? Any help is appreciated.

Thanks for the help, guys :)

Oh, and also, what's 2^x = (1/64)?

actually I have a few more...

1) Find the value of "n" in the equation. n =log100

2) log[n]243=5 with "n" being the base

3)Using the inverse property of exponents and logarithms, simplify the expression.

log[6]6^3

4) Simplify the expression. e^(2ln3)

sorry. That seems like a lot, but this will determine if I pass or fail math. I 100% appreciate any responses. Please include work. :)

Answer 1

Well, almost.

A = P(1 + r)^n

P = original population ( 5600 )
r = annual increase ( .095 )
n = number of years ( 10 )

You always want r to be the growth rate per compounding interval, and n to be the number of compounding intervals. Since your growth rate is annual (that is, yearly )and you want to know what's happening in some number of years, r doesn't get divided by anything.

Answer 2

P0 = 5600
P1 = 5600 * (1.095)
P2 = 5600 * (1.095)^2
P3 = 5600 * (1.095)^3
.
.
.
P10 = 5600 * (1.095)^10