Assessment Questions

1. Simplify: \( 2^3 \cdot 2^{-5} \)
2. Simplify: \( (3x^2)^3 \cdot x^{-2} \)
3. Evaluate: \( 4^0 \), \( 5^{-2} \)
4. Exponential growth: Population 1,200, doubles every 25 years. Population after 50 years?
5. Graph \( y = 3^x \) and \( y = 2 \cdot 3^x \) on same axes.
6. Compound interest: $3,000 at 4% yearly for 7 years. Find total.
7. Radioactive decay: half-life 8 hours, initial mass 64g. Remaining after 24 hours?
8. Solve: \( 2^{x+1} = 16 \)
9. Population triples every 10 years. Write function and find population after 30 years.
10. Describe behavior of \( y = 5 \cdot 2^x \) as \( x \to \infty \) and \( x \to -\infty \).