Exponential Functions and the Number e: Algebra 2 Math Test – PDF Download

Question 1: Growth model (2 points)

The population of a city is modeled by \(P(t)=18000(1.045)^{t}\), where \(t\) is in years.

1. State the initial population and the yearly percent growth. (1 point)
2. Find the population after 8 years, to the nearest whole number. (1 point)

Question 2: Compound interest (2 points)

Jamal invests $2,400 at 3.2% interest compounded monthly for 5 years.

1. Write the balance formula. (1 point)
2. Find the balance to the nearest cent. (1 point)

Question 3: Continuous versus yearly (2 points)

Mei invests $1,800 at 4.5% for 12 years.

1. Find the balance with continuous compounding. (1 point)
2. Find the balance with yearly compounding and how much less it is. (1 point)

Question 4: Model from a graph (3 points)

The graph of \(f(x)=a\cdot b^{x}\) is shown.

1. Find \(a\) and \(b\). (1 point)
2. Write the equation. (1 point)
3. Find \(f(4)\). (1 point)

Question 5: Solve for time (3 points)

An account follows \(A(t)=2000(1.04)^{t}\) dollars after \(t\) years.

1. Solve \(2000(1.04)^{t}=3500\) exactly. (1 point)
2. Give the solution to the nearest hundredth. (1 point)
3. After how many full years does the balance first exceed $3,500? Justify. (1 point)

Question 6: Doubling time (2 points)

An investment grows by 6% each year. Find its doubling time to the nearest hundredth of a year.

Question 7: Half-life (3 points)

The graph shows the mass of a radioactive sample.

1. Read the half-life from the graph. (1 point)
2. Write a model for the mass \(A(t)\) after \(t\) days. (1 point)
3. Find the mass after 12 days, to the nearest tenth of a mg. (1 point)

Question 8: Equivalent forms (3 points)

A quantity follows \(f(t)=500(1.12)^{t}\) with \(t\) in years.

1. State the yearly percent growth rate. (1 point)
2. Write an equivalent form \(500e^{kt}\) and give \(k\) to four decimal places. (1 point)
3. Find the equivalent monthly growth rate as a percent, to the nearest hundredth. (1 point)

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