Precalculus Exponential Functions and the Number e Quiz: 10 Questions with Explanations

A \(y=40(1.9)^{x}\)B \(y=0.9\cdot 40^{x}\)C \(y=40(0.9)^{x}\)D \(y=40x^{0.9}\)

A base between 0 and 1 gives decay. 1.9 would be 90 percent growth.

A 0.06B 0.94C 6D 1.06

Growth factor = 1 + rate = 1.06.

A 250B 1,000C 30D 125

5^3 = 125, then times 2 gives 250. Computing (2 times 5)^3 = 1,000 is a mistake.

A \(y=-4\)B \(y=4\)C \(y=0\)D \(x=-4\)

The graph is the parent shifted down 4, so the asymptote is y = -4.

A \(y=10\cdot2^{x}\)B \(y=5\cdot2^{x}\)C \(y=5x+5\)D \(y=5\cdot10^{x}\)

a = f(0) = 5 and b = 10/5 = 2.

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

Continuous compounding is the limit of the n-times formula, which gives A = Pe^(rt).

A Yearly compoundingB Continuous compoundingC Monthly compoundingD They are all equal

More frequent compounding earns more, and continuous compounding is the limit.

A \(25\text{ g}\)B \(50\text{ g}\)C \(12.5\text{ g}\)D \(0\text{ g}\)

6 days is two half-lives: 100, 50, 25. Using one half-life gives 50.

A 110B 0C 70D 180

As t grows, 0.9^t goes to 0, so the output approaches 70.

A 3.141B 2.718C 1.618D 2.5

e is about 2.71828. The value 3.14 is pi.