Chapter 6 Review Problems

1. Simplify: \( 3^4 \cdot 3^{-2} \)
2. Simplify: \( (2x^3y)^2 \cdot x^{-1} \)
3. Evaluate: \( 5^0 \), \( 2^{-3} \)
4. Write an exponential function for a population doubling every 15 years. Find population after 45 years.
5. Graph \( y = 2^x \) and \( y = 0.5 \cdot 2^x \) on the same axes.
6. Compound interest: $2,500 at 3% annually for 8 years. Find total.
7. Population growth: 400 bacteria triples every 4 hours. Find population after 12 hours.
8. Radioactive decay: half-life 10 hours, initial mass 100g. Remaining after 30 hours?
9. Solve: \( 5^{x-1} = 125 \)
10. Describe the behavior of \( y = 7 \cdot 3^x \) as \( x \to \infty \) and \( x \to -\infty \).