Review Problems

1. Simplify: \( 2^3 \cdot 2^5 \)
2. Simplify: \( (x^4 y^3)^2 \)
3. Evaluate: \( 5^0 \), \( 2^{-3} \)
4. Write an exponential function for a population doubling every 6 hours.
5. Graph \( y = 2^x \) and \( y = 3 \cdot 2^x \).
6. Compound interest: $1,000 at 5% annually, find amount after 10 years.
7. Population of 800 bacteria triples every 4 hours, find population after 12 hours.
8. Radioactive decay: half-life of 8 hours, initial 64g, find remaining after 24 hours.
9. Solve: \( 2^{x+1} = 16 \)
10. Graph exponential growth and describe the behavior of the function over time.