Algebra 1 Exponential Functions and Growth Worksheet (PDF)

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

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This algebra 1 exponential functions worksheet 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.

These 20 problems practice exponential functions and growth (Common Core F-LE.A.1, F-LE.A.2, F-LE.A.3, and F-IF.C.8b). You will identify growth and decay factors, graph exponential functions, compare linear and exponential growth, and model compound interest and half-life. The first problems are short skill checks, and the last six are word problems that need several steps. Work in order and show every line of your work, because a bare answer earns little credit on a test.

Algebra 1 · Common Core State Standards: F-LE.A.1, F-LE.A.2, F-LE.A.3, F-IF.C.7e, F-IF.C.8b

Algebra 1 exponential functions worksheet: exercises 1 to 10

Exercise 1 – Identify a and b

Identify the starting value and the growth factor of $y = 3 \cdot 2^{x}$. Is it growth or decay?

Exercise 2 – Decay factor

Identify the decay factor of $y = 5(0.8)^{x}$ and the percent decrease per step.

Exercise 3 – Complete a table

Complete the table.

Evaluate $y = 4 \cdot 3^{x}$ for $x = 0, 1, 2, 3$.

Exercise 4 – Exponential table

A table of values.

Show that the table is exponential and find the common ratio.

Exercise 5 – Linear table

A table of values.

Is the function linear or exponential? Explain.

Exercise 6 – Write from a table

A table shows $x = 0, 1, 2$ with $y = 5, 10, 20$. Write the exponential function.

Exercise 7 – Graph a growth function

Graph $y = 2^{x}$ using the points with $x = -2, -1, 0, 1, 2, 3$.

Exercise 8 – Graph a decay function

Graph $y = \left(\frac{1}{2}\right)^{x}$ for $x = -2$ to $x = 3$.

Exercise 9 – Rate to factor

Write the growth or decay factor for (a) 12% growth, (b) 8% decay.

Exercise 10 – Evaluate with a calculator

Evaluate $y = 100(1.05)^{x}$ at $x = 10$. Round to the nearest hundredth.

Exercises 11 and up

Exercise 11 – Intercept and asymptote

For $y = 2^{x}$, give the y-intercept, the domain, the range, and describe the behavior as $x$ becomes very negative.

Exercise 12 – Solve an exponential equation

Solve $2^{x} = 32$ and $3^{x} = 81$.

Exercise 13 – Linear versus exponential

Compare $f(x) = 10x + 5$ and $g(x) = 2^{x}$ at $x = 10$.

Exercise 14 – Domain and range

State the domain and range of $y = 3 \cdot 2^{x}$.

Exercise 15 – Rewrite the base

Rewrite $y = 2^{3t}$ in the form $y = b^{t}$ and give the growth factor per unit of $t$.

Exercise 16 – Town population

Population growth of 4% per year.

A town of 20,000 people grows 4% per year. Write a model and find the population after 5 years, to the nearest person.

Exercise 17 – Car value

Car value by year.

A $24,000 car loses 15% of its value each year. Write a model and find its value after 3 years.

Exercise 18 – Compound interest

Sofia deposits $1,500 at 6% interest compounded annually. Find the amount after 8 years.

Exercise 19 – Medicine half-life

Amount of medicine left.

A 80 mg dose of medicine has a half-life of 6 hours, so $A = 80\left(\frac{1}{2}\right)^{t/6}$. Find the amount left after 18 hours.

Exercise 20 – Viral video

Views for two videos.

Video A has 50 views and triples every day: $A = 50 \cdot 3^{d}$. Video B has 50 views and gains 200 per day: $B = 50 + 200d$. Compare them on days 2 and 3.

Exercise 21 – Doubling time

Liam invests $2,000 that doubles every 12 years, so $A = 2000 \cdot 2^{t/12}$. After how many years is the value $8,000?

Key facts behind this algebra 1 exponential functions worksheet

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 worksheet

Work through the exercises in order: they go from simple to challenging. Write every step on paper, then compare with the solutions page and redo any exercise you missed the next day.

Download the algebra 1 exponential functions worksheet as a PDF with the button below and keep it with your notes.

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