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.)