Exponential Functions Praxis

Let $f(x)=2^x$, $g(x)=\left(\frac{4}{5}\right)^{x-2}$, $h(x)=1.07^{3x}$. Compute the following and simplify when possible:

1. $f(1)$
2. $g(3)$
3. $f(0)$
4. $h(4)$
5. $g(4)$
6. $h(0.5)$

For each of the following functions, list the simple exponential function (of the form $a^x$ for some $a$), list the ways said function was transformed IN THE CORRECT ORDER, and then graph the function (using the control point method).

7. $f(x)=3^{x-2}$
8. $g(x)=2\cdot 4^{x+1}$
9. $h(t)= \left(\frac{2}{3}\right)^{t+5}-2$
10. $f(t)=-2\cdot 3^{t+2}+3$
11. $f(x)=-3\cdot \left(\frac{1}{2}\right)^{-x+4}-2$

Honors problem 1.) $f(x)=2\cdot \left(\frac{3}{2}\right)^{-3x+1}+2$

12. Suppose you put $1000 into an account that yields 6% per year compounded daily. How much will you have after 5 year and after 20 years?
13. Suppose you put $150 into an investment account that has an annual rate of return of 10% per year, compounded quarterly. How much money will be in the account in 15 years and in 40 years?
14. Suppose you take out a loan against your life insurance policy worth $50,000. Given that you don’t have to make regular payments into the account, the account will simply accrue interest at a rate of 2.2% per year, compounded continuously. How much will you owe after 10 years of not making any payments?

Honors problem 2.) Suppose you invest your money in a stock market index fund that has an average rate of return of $9%$ per year (compounded yearly). How long will it take to double your money at that rate? (Note: enough information is given in this problem to solve it.)