Algebra 2 Exponential Growth and Decay Test with Point Values (PDF)

Algebra 2 math test: Exponential Growth and Decay – Maths PDF

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This algebra 2 exponential functions test for Algebra 2 covers exponential growth and decay (Common Core F-LE.A.2, F-LE.B.5, A-SSE.B.3c, F-IF.C.8b), with a free PDF to print.

This 45-minute test on exponential growth and decay has 9 questions worth 20 points in total. The questions move from direct skills to multi-step problems. Show your work, because partial credit is given for a correct setup and sound reasoning.

Time and points

About this test

Grade: Algebra 2
Chapter: Exponential Growth and Decay
Standards: F-LE.A.2, F-LE.B.5, A-SSE.B.3c, F-IF.C.8b
Time: 45 minutes
Total: 20 points

Algebra 2 exponential functions test: questions

Question 1 – Identify and evaluate [2 pts]

For $f(x) = 6(0.5)^{x}$, state whether it is growth or decay and find $f(3)$.

Question 2 – Table to function [3 pts]

Values of f.

Write an exponential function for the table and find $f(5)$.

Question 3 – Percent growth [2 pts]

A city of 8,000 people grows 6% per year. Write a function and find the population after 3 years.

Question 4 – Compound interest [3 pts]

Mei invests $3,000 at 6% for 4 years. Find the balance if the interest is compounded (a) annually and (b) quarterly.

Question 5 – Half-life [2 pts]

A radioactive sample of 200 g has half-life 5 years. How much remains after 15 years?

Question 6 – Graph features [2 pts]

Graph of an exponential function.

The graph of $f(x) = 3(0.5)^{x}$ is shown. Give its y-intercept, asymptote, and end behavior as $x$ increases.

Question 7 – Equivalent rate [2 pts]

A bank pays 0.5% per month, so a balance grows as $1.005^{12t}$. Rewrite it as $b^{t}$ and find the annual rate to the nearest tenth of a percent.

Question 8 – Linear versus exponential [2 pts]

Plan A (solid) and Plan B (dashed).

Plan A is $A = 100 + 30w$ and Plan B is $B = 10 \cdot 2^{w}$. Use the graph or a table to find the first whole week when Plan B is larger.

Question 9 – Find the error [2 pts]

Jamal says $f(x) = 500(0.9)^{x}$ loses 0.9% each step. Explain the error and give the correct rate.

Key facts behind this algebra 2 exponential functions test

Key facts

f(x) = a·b^x: a is the initial value, b the growth factor.
Growth factor b = 1 + r (growth) or 1 – r (decay).
Equal steps in x multiply the output by b.
Compound interest: A = P(1 + r/n)^(nt); continuous: A = Pe^(rt).
Rewrite b^x expressions to find equivalent rates.

How to use this algebra 2 exponential functions test

Time yourself: the test is designed for an average student in 45 minutes. Answer the questions you are sure of first, then come back to the longer ones and check your units.

All Algebra 2 chapters: Algebra 2 math.

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