Homework

Problem 1 · easy

Simplify: 3^4 * 3^(-2).

Problem 2 · easy

Evaluate: 8^(2/3).

Problem 3 · medium

Evaluate: 16^(-3/4).

Problem 4 · easy

Is f(x) = 3^x growth or decay? State domain and range.

Problem 5 · easy

Is f(x) = (0.5)^x growth or decay? State domain and range.

Problem 6 · easy

Evaluate e^0 and e^1 (exact values, then approximate e^1 to 3 decimal places).

Problem 7 · easy

State the horizontal asymptote of f(x) = 5^x.

Problem 8 · easy

Describe the transformation: g(x) = 2^x - 3 relative to f(x) = 2^x.

Problem 9 · easy

State the new HA of g(x) = 2^x - 3.

Problem 10 · medium

Describe: g(x) = e^(x+2) + 1.

Problem 11 · easy

Solve: 3^x = 81.

Problem 12 · easy

Solve: 4^(x-1) = 16.

Problem 13 · medium

Solve: (1/2)^x = 32.

Problem 14 · medium

Solve: 27^x = 9. Express x as a fraction.

Problem 15 · medium

$2000 is invested at 4% compounded quarterly for 10 years. Find A (round to the nearest cent).

Problem 16 · medium

$5000 is invested at 3% continuously compounded for 8 years. Find A (use e^0.24 ≈ 1.2712).

Problem 17 · medium

A radioactive element has half-life 10 years. Starting with 100g, how much remains after 30 years?

Problem 18 · medium

A bacteria colony doubles every 3 hours. Starting with 500 bacteria, how many after 12 hours?

Problem 19 · easy

Find the y-intercept of g(x) = 3 * e^x - 1.

Problem 20 · easy

Solve 2^(3x) = 2^(x+4).

Problem 21 · medium

Which grows faster for large x: f(x) = x^10 or g(x) = 2^x?

Problem 22 · easy

The population of a city is modeled by P(t) = 50000 * e^(0.02t). What is the population at t=0?

Problem 23 · medium

For P(t) = 50000 * e^(0.02t), what is the approximate population after 10 years? (Use e^0.2 ≈ 1.2214)

Problem 24 · medium

Solve: 5^(2x+1) = 125.

Problem 25 · challenge

Compare: which is larger, e^3 or 3^e? (Use e ≈ 2.718, e^3 ≈ 20.09, 3^e ≈ 3^2.718 ≈ 19.81)