Grade 12 Exponential Equations Worksheet

Exponential Equations Review

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. Solve for x in the equation: 3^(2x-1) = 27

2. Solve for x in the equation: e^(x+2) = 5

3. Which of the following graphs represents exponential decay?

4. The horizontal asymptote of the function f(x) = 2^x is at y =  .

5. The base of the natural logarithm is represented by the constant  .

6. The domain of any exponential function f(x) = a^x (where a > 0, a ≠ 1) is all real numbers.

7. Sketch the graph of the function y = (1/2)^x on the coordinate plane below. Label at least two points and the asymptote.

8. A population of bacteria doubles every hour. If there are initially 100 bacteria, how many will there be after 5 hours? Use the formula P(t) = P₀ * 2^(t/h), where h is the doubling time.