Algebra 1 Exponential Functions and Growth Quiz: 10 Questions with Explanations

A \(y = 2(1.5)^{x}\)B \(y = 2(0.5)^{x}\)C \(y = 2 + 1.5x\)D \(y = 1.5 + 2x\)

Only y = 2(1.5)^x has a variable exponent and a base greater than 1.

A 0.07B 0.93C 1.07D 7

Growth factor = 1 + rate = 1 + 0.07 = 1.07.

A \(y = 4x + 4\)B \(y = 2 \cdot 4^{x}\)C \(y = 4 \cdot 2^{x}\)D \(y = 4 + 2^{x}\)

The starting value is 4 and each step doubles.

A Exponential growthB Exponential decayC Linear with negative slopeD Quadratic

The curve falls, flattens toward the x-axis, and never reaches it, which is exponential decay.

A \(x = 9\)B \(x = 3\)C \(x = 24\)D \(x = 30\)

Since 27 = 3³, x = 3. Dividing 27 by 3 gives 9 and is not correct.

A \(1000(0.05)^{4}\)B \(1000 + 0.05(4)\)C \(1000(1.5)^{4}\)D \(1000(1.05)^{4}\)

A = P(1 + r)^t with r = 0.05 and t = 4.

A Linear, because it adds 5 each timeB Exponential, because it increasesC Exponential, because the ratio is 5D Neither

The differences are all 5, so it is linear. The ratios 11/6, 16/11, 21/16 are not constant.

A 75%B 25%C 0.75%D 125%

The decay factor 0.75 means it keeps 75% and loses 25%.

A 8 gramsB 32 gramsC 16 gramsD 4 grams

Six days is 3 half-lives: 64 → 32 → 16 → 8.

A \((0, 2)\)B \((1, 0)\)C \((0, 0)\)D \((0, 1)\)

At x = 0, 2⁰ = 1, so the curve crosses the y-axis at (0, 1).