Algebra 1 Exponential Functions and Growth Test with Point Values (PDF)

Algebra 1 math test: Exponential Functions and Growth – Maths PDF

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This algebra 1 exponential functions test for Algebra 1 covers exponential functions and growth (Common Core F-LE.A.1, F-LE.A.2, F-LE.A.3, F-IF.C.7e, F-IF.C.8b), with a free PDF to print.

This 45-minute test on exponential functions and growth covers Common Core F-LE.A.1, F-LE.A.2, F-LE.A.3, and F-IF.C.8b and is worth 20 points. Work alone, show all steps, and use a calculator only if your teacher allows it. Partial credit is given for correct work, so write down your reasoning even when you are unsure of the final answer.

Time and points

About this test

Grade: Algebra 1
Chapter: Exponential Functions and Growth
Standards: F-LE.A.1, F-LE.A.2, F-LE.A.3, F-IF.C.7e, F-IF.C.8b
Time: 45 minutes
Total: 20 points

Algebra 1 exponential functions test: questions

Question 1 – Growth or decay [2 pts]

State whether each function models growth or decay and give the percent change per step.

$y = 4(1.3)^{x}$ (1 point)
$y = 7(0.6)^{x}$ (1 point)

Question 2 – Evaluate [2 pts]

Let $f(x) = 5 \cdot 2^{x}$. Find $f(4)$ and $f(-1)$.

Question 3 – Write from a table [2 pts]

Table for question 3.

The table shows an exponential function. Write its equation.

Question 4 – Graph a decay function [2 pts]

Grid for question 4.

Graph $y = 3\left(\frac{1}{2}\right)^{x}$ by plotting the points for $x = -1, 0, 1, 2$.

Question 5 – Savings growth [2 pts]

A savings account has $500 and earns 8% per year, compounded annually.

Write a function for the amount after $t$ years. (1 point)
Find the amount after 3 years, to the nearest cent. (1 point)

Question 6 – Solve [2 pts]

Solve each equation.

$5^{x} = 125$ (1 point)
$2^{x+1} = 16$ (1 point)

Question 7 – Car depreciation [3 pts]

A car’s value in dollars is $V = 30000(0.9)^{t}$ after $t$ years.

What percent does the car lose each year? (1 point)
Find the value after 4 years. (1 point)
In which year does the value first drop below $20,000? (1 point)

Question 8 – Linear versus exponential [3 pts]

Two savings plans.

Plan A saves $100 and adds $50 each week. Plan B saves $10 and doubles each week. The table shows the amounts.

Which plan has more money in week 5? (1 point)
Which plan has more money in week 6? (1 point)
Explain why Plan B eventually stays ahead. (1 point)

Question 9 – Half-life [2 pts]

A 120 mg dose has a half-life of 4 hours. Write a function for the amount after $t$ hours and find the amount after 12 hours.

Key facts behind this algebra 1 exponential functions test

Key facts

Exponential form: f(x) = a·bˣ with a the starting value and b the factor.
Growth: b = 1 + r. Decay: b = 1 – r.
Linear functions add a constant; exponential functions multiply by a constant.
Compound interest: A = P(1 + r)ᵗ.
An exponential function eventually exceeds any linear function.

How to use this algebra 1 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 1 chapters: Algebra 1 math.

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