Algebra 2 Exponential Growth and Decay Quiz: 10 Questions with Explanations

A \(1.08\)B \(7\)C \(0.08\)D \(8\)

In a·b^x, b = 1.08 is the factor. The rate is 8%, and 7 is the initial value.

A 0.04B 1.04C 0.96D 4

Growth of 4% means 100% + 4% = 104% = 1.04.

A \(900(0.88)^{t}\)B \(900(0.12)^{t}\)C \(900(1.12)^{t}\)D \(900 – 0.12t\)

A 12% decrease leaves 88% each year, so b = 0.88.

A \(f(x) = 2 + 4x\)B \(f(x) = 3 \cdot 2^{x}\)C \(f(x) = 2 \cdot 3^{x}\)D \(f(x) = 2x^{3}\)

The ratio is 3 and the initial value is 2.

A \(x = 0\)B \(y = 2\)C \(y = 0\)D \(There is none\)

The curve approaches the x-axis on the left but never touches it.

A \(A = P(1 + r)^{12t}\)B \(A = P\left(1 + \frac{r}{t}\right)^{12}\)C \(A = P + 12rt\)D \(A = P\left(1 + \frac{r}{12}\right)^{12t}\)

There are 12 periods per year, each with rate r/12.

A \(\frac{1}{6}\)B \(\frac{1}{8}\)C \(\frac{1}{3}\)D \(\frac{3}{2}\)

Each half-life halves the amount: 1/2 · 1/2 · 1/2 = 1/8.

A \(2^{2x}\)B \(2^{x}\)C \(2^{x + 2}\)D \(8^{x}\)

4 = 2², so 4^x = (2²)^x = 2^(2x).

A The linear function always stays largerB They are always equalC The exponential function stops growingD The exponential function eventually exceeds the linear function

Multiplying by a constant factor each step eventually outgrows adding a constant amount.

A The quantity loses 75% each periodB The quantity loses 25% each periodC The quantity gains 25% each periodD The quantity loses 0.75 each period

b = 0.75 = 1 – 0.25, so the decrease is 25% per period.