Through (0, 2) and (1, 6); asymptote y = 0

Through (0, 3/4) and (1, 3); asymptote y = 0

If y is the value of a house, in thousands of dollars, x years after 1900, a model is y = 58.4(1.04)^x. What does the y-intercept mean?

In 1900 the house was worth about $58,400.

A savings account starts at 40000 dollars and grows by 8% each year. Make a table for years 0 to 4, to the nearest whole number, and plot the points.

(0, 40000), (1, 43200), (2, 46656), (3, 50388), (4, 54420)

Exponential growth and decay worksheet for Algebra 1

A quantity that grows by the same percent each period is exponential: y = a(1 + r)^x with a the starting amount and r the rate. Decay is the same with 1 - r. The base tells you which: bigger than 1 grows, between 0 and 1 decays, and the distance from 1 is the rate.

Also taught in Algebra 2, at its own level and with its own examples.

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Sigma Prep · sigmaprep.io/worksheets Name Exponential Growth and Decay Date Period Answer each question. Identify growth or decay and the rate Classify as growth or decay, and give the percent rate: $P (t) = 1200 {(1.08)}^{t}$ . Tell whether $f (x) = 4000 {(1.03)}^{x}$ shows growth or decay, and by what percent. Does $A (t) = 2600 {(0.98)}^{t}$ show growth or decay? By what percent? Classify as growth or decay, and give the percent rate: $y = 4800 {(1.02)}^{x}$ . Does $y = 3000 {(0.96)}^{x}$ show growth or decay? By what percent? Write the function from a rate A colony of $3200$ bacteria grows by $30 %$ each hour. Write $y$ after $x$ hours. A car worth $$ 3200$ loses value by $3 %$ each year. Write $y$ after $x$ years. A town of $4500$ people shrinks by $4 %$ each year. Write $y$ after $x$ years. A forest of $1500$ trees shrinks by $8 %$ each year. Write $y$ after $x$ years. A forest of $2400$ trees grows by $4 %$ each year. Write $y$ after $x$ years. Find the amount after some time A colony of $1500$ bacteria grows by $3 %$ each hour. About how many after $7$ hours? Round to the nearest whole number. A stock of $3200$ fish shrinks by $3 %$ each year. About how many after $12$ years? Round to the nearest whole number. A forest of $4500$ trees grows by $3 %$ each year. About how many after $10$ years? Round to the nearest whole number. A forest of $1800$ trees shrinks by $8 %$ each year. About how many after $8$ years? Round to the nearest whole number. A town of $1500$ people grows by $8 %$ each year. About how many after $8$ years? Round to the nearest whole number. Find the $y$ -intercept and asymptote Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{3})}^{x} + 2$ Find the $y$ -intercept and the asymptote of $y = 5 \cdot {(\frac{1}{5})}^{x} + 6$ Find the $y$ -intercept and the asymptote of $y = 3 \cdot {(\frac{1}{2})}^{x} - 1$ Find the $y$ -intercept and the asymptote of $y = 8 \cdot 2^{x} - 6$ Find the $y$ -intercept and the asymptote of $y = 6 \cdot 3^{x} + 6$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exponential Growth and Decay

Date Period

Answer each question.

Identify growth or decay and the rate
Classify as growth or decay, and give the percent rate: $P (t) = 1200 {(1.08)}^{t}$ .
Tell whether $f (x) = 4000 {(1.03)}^{x}$ shows growth or decay, and by what percent.
Does $A (t) = 2600 {(0.98)}^{t}$ show growth or decay? By what percent?
Classify as growth or decay, and give the percent rate: $y = 4800 {(1.02)}^{x}$ .
Does $y = 3000 {(0.96)}^{x}$ show growth or decay? By what percent?

Write the function from a rate
A colony of $3200$ bacteria grows by $30 %$ each hour. Write $y$ after $x$ hours.
A car worth $$ 3200$ loses value by $3 %$ each year. Write $y$ after $x$ years.
A town of $4500$ people shrinks by $4 %$ each year. Write $y$ after $x$ years.
A forest of $1500$ trees shrinks by $8 %$ each year. Write $y$ after $x$ years.
A forest of $2400$ trees grows by $4 %$ each year. Write $y$ after $x$ years.

Find the amount after some time
A colony of $1500$ bacteria grows by $3 %$ each hour. About how many after $7$ hours? Round to the nearest whole number.
A stock of $3200$ fish shrinks by $3 %$ each year. About how many after $12$ years? Round to the nearest whole number.
A forest of $4500$ trees grows by $3 %$ each year. About how many after $10$ years? Round to the nearest whole number.
A forest of $1800$ trees shrinks by $8 %$ each year. About how many after $8$ years? Round to the nearest whole number.
A town of $1500$ people grows by $8 %$ each year. About how many after $8$ years? Round to the nearest whole number.

Find the $y$ -intercept and asymptote
Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{3})}^{x} + 2$
Find the $y$ -intercept and the asymptote of $y = 5 \cdot {(\frac{1}{5})}^{x} + 6$
Find the $y$ -intercept and the asymptote of $y = 3 \cdot {(\frac{1}{2})}^{x} - 1$
Find the $y$ -intercept and the asymptote of $y = 8 \cdot 2^{x} - 6$
Find the $y$ -intercept and the asymptote of $y = 6 \cdot 3^{x} + 6$



Sigma Prep · sigmaprep.io/worksheets Name Exponential Growth and DecayAnswer keyVersion 1 Date Period Answer each question. Identify growth or decay and the rate Classify as growth or decay, and give the percent rate: $P (t) = 1200 {(1.08)}^{t}$ .Growth, $8 %$ Tell whether $f (x) = 4000 {(1.03)}^{x}$ shows growth or decay, and by what percent.Growth, $3 %$ Does $A (t) = 2600 {(0.98)}^{t}$ show growth or decay? By what percent?Decay, $2 %$ Classify as growth or decay, and give the percent rate: $y = 4800 {(1.02)}^{x}$ .Growth, $2 %$ Does $y = 3000 {(0.96)}^{x}$ show growth or decay? By what percent?Decay, $4 %$ Write the function from a rate A colony of $3200$ bacteria grows by $30 %$ each hour. Write $y$ after $x$ hours. $y = 3200 {(1.3)}^{x}$ A car worth $$ 3200$ loses value by $3 %$ each year. Write $y$ after $x$ years. $y = 3200 {(0.97)}^{x}$ A town of $4500$ people shrinks by $4 %$ each year. Write $y$ after $x$ years. $y = 4500 {(0.96)}^{x}$ A forest of $1500$ trees shrinks by $8 %$ each year. Write $y$ after $x$ years. $y = 1500 {(0.92)}^{x}$ A forest of $2400$ trees grows by $4 %$ each year. Write $y$ after $x$ years. $y = 2400 {(1.04)}^{x}$ Find the amount after some time A colony of $1500$ bacteria grows by $3 %$ each hour. About how many after $7$ hours? Round to the nearest whole number. $1,845$ A stock of $3200$ fish shrinks by $3 %$ each year. About how many after $12$ years? Round to the nearest whole number. $2,220$ A forest of $4500$ trees grows by $3 %$ each year. About how many after $10$ years? Round to the nearest whole number. $6,048$ A forest of $1800$ trees shrinks by $8 %$ each year. About how many after $8$ years? Round to the nearest whole number. $924$ A town of $1500$ people grows by $8 %$ each year. About how many after $8$ years? Round to the nearest whole number. $2,776$ Find the $y$ -intercept and asymptote Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{3})}^{x} + 2$ $(0, 3)$ , $y = 2$ Find the $y$ -intercept and the asymptote of $y = 5 \cdot {(\frac{1}{5})}^{x} + 6$ $(0, 11)$ , $y = 6$ Find the $y$ -intercept and the asymptote of $y = 3 \cdot {(\frac{1}{2})}^{x} - 1$ $(0, 2)$ , $y = - 1$ Find the $y$ -intercept and the asymptote of $y = 8 \cdot 2^{x} - 6$ $(0, 2)$ , $y = - 6$ Find the $y$ -intercept and the asymptote of $y = 6 \cdot 3^{x} + 6$ $(0, 12)$ , $y = 6$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Exponential Growth and DecayAnswer keyVersion 1

Date Period

Answer each question.

Identify growth or decay and the rate
Classify as growth or decay, and give the percent rate: $P (t) = 1200 {(1.08)}^{t}$ .Growth, $8 %$
Tell whether $f (x) = 4000 {(1.03)}^{x}$ shows growth or decay, and by what percent.Growth, $3 %$
Does $A (t) = 2600 {(0.98)}^{t}$ show growth or decay? By what percent?Decay, $2 %$
Classify as growth or decay, and give the percent rate: $y = 4800 {(1.02)}^{x}$ .Growth, $2 %$
Does $y = 3000 {(0.96)}^{x}$ show growth or decay? By what percent?Decay, $4 %$

Write the function from a rate
A colony of $3200$ bacteria grows by $30 %$ each hour. Write $y$ after $x$ hours. $y = 3200 {(1.3)}^{x}$
A car worth $$ 3200$ loses value by $3 %$ each year. Write $y$ after $x$ years. $y = 3200 {(0.97)}^{x}$
A town of $4500$ people shrinks by $4 %$ each year. Write $y$ after $x$ years. $y = 4500 {(0.96)}^{x}$
A forest of $1500$ trees shrinks by $8 %$ each year. Write $y$ after $x$ years. $y = 1500 {(0.92)}^{x}$
A forest of $2400$ trees grows by $4 %$ each year. Write $y$ after $x$ years. $y = 2400 {(1.04)}^{x}$

Find the amount after some time
A colony of $1500$ bacteria grows by $3 %$ each hour. About how many after $7$ hours? Round to the nearest whole number. $1,845$
A stock of $3200$ fish shrinks by $3 %$ each year. About how many after $12$ years? Round to the nearest whole number. $2,220$
A forest of $4500$ trees grows by $3 %$ each year. About how many after $10$ years? Round to the nearest whole number. $6,048$
A forest of $1800$ trees shrinks by $8 %$ each year. About how many after $8$ years? Round to the nearest whole number. $924$
A town of $1500$ people grows by $8 %$ each year. About how many after $8$ years? Round to the nearest whole number. $2,776$

Find the $y$ -intercept and asymptote
Find the $y$ -intercept and the asymptote of $y = {(\frac{1}{3})}^{x} + 2$ $(0, 3)$ , $y = 2$
Find the $y$ -intercept and the asymptote of $y = 5 \cdot {(\frac{1}{5})}^{x} + 6$ $(0, 11)$ , $y = 6$
Find the $y$ -intercept and the asymptote of $y = 3 \cdot {(\frac{1}{2})}^{x} - 1$ $(0, 2)$ , $y = - 1$
Find the $y$ -intercept and the asymptote of $y = 8 \cdot 2^{x} - 6$ $(0, 2)$ , $y = - 6$
Find the $y$ -intercept and the asymptote of $y = 6 \cdot 3^{x} + 6$ $(0, 12)$ , $y = 6$

How to do these

$y = 500 {(0.92)}^{x}$

The base is 0.92, which is less than 1, so it decays.
1 - 0.92 is 0.08, which is 8 percent.

The answer is Decay, $8 %$ .

Where students go wrong

Reading 0.92 as a 92 percent rate. The rate is how far the base sits from 1, not the base itself.

Also called exponential functions, growth and decay, percent growth or exponential decay.

What you can put on this worksheet

Growth or decay, and the rate: Tell whether $f (x) = 300 {(0.9)}^{x}$ shows growth or decay, and by what percent. → Decay, $10 %$
Write the function from a rate: A town of $250$ people shrinks by $25 %$ each year. Write $y$ after $x$ years. → $y = 250 {(0.75)}^{x}$
The amount after some time: A stock of $250$ fish shrinks by $25 %$ each year. About how many after $2$ years? Round to the nearest whole number. → $141$
The y-intercept and the asymptote: Find the $y$ -intercept and the asymptote of $y = 3 \cdot 4^{x}$ → $(0, 3)$ , $y = 0$
Write y = ab^x from two points or a graph: The graph is $y = a b^{x}$ . Use the marked points to write its equation. → $y = 3 \cdot 3^{x}$
Graph an exponential function: Graph $y = 2 {(3)}^{x}$ → Through $(0, 2)$ and $(1, 6)$ ; asymptote $y = 0$
The years given as dates: Sales were $5160$ units in 2015, and the number grows by $5 %$ each year. Estimate the number of units in 2017, to the nearest whole number. → $5689$
A fraction in front, a fraction base, a negative power: Given $g (n) = 2 \cdot 3^{n}$ , find $g (- 2)$ → $\frac{2}{9}$
Graph with a fraction in front: Graph $y = \frac{3}{4} {(4)}^{x}$ → Through $(0, \frac{3}{4})$ and $(1, 3)$ ; asymptote $y = 0$
The equation of a decay graph: Write the equation $y = a b^{x}$ of the graph → $y = 6 ⁣ {(\frac{2}{3})}^{x}$
An exponential model: its start, its rate, a prediction, a year: If $y$ is the value of a house, in thousands of dollars, $x$ years after 1900, a model is $y = 58.4 {(1.04)}^{x}$ . What does the $y$ -intercept mean? → In 1900 the house was worth about $58,400.
A table of values, plotted: A savings account starts at $40000$ dollars and grows by $8 %$ each year. Make a table for years 0 to 4, to the nearest whole number, and plot the points. → $(0, 40000),$ $(1, 43200),$ $(2, 46656),$ $(3, 50388),$ $(4, 54420)$

Questions about these worksheets

Yes. Every exponential growth and decay sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 1 is usually taken around 8th or 9th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the exponential growth and decay questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 12: growth or decay, and the rate, write the function from a rate, the amount after some time, the y-intercept and the asymptote, write y = ab^x from two points or a graph, graph an exponential function, the years given as dates, a fraction in front, a fraction base, a negative power, graph with a fraction in front, the equation of a decay graph, an exponential model: its start, its rate, a prediction, a year and a table of values, plotted. Tick as many as you want and set how many of each, or let it spread them evenly.

Reading 0.92 as a 92 percent rate. The rate is how far the base sits from 1, not the base itself.

Exponential growth and decay worksheet for Algebra 1

Select your difficulty

Identify growth or decay and the rate

Write the function from a rate

Find the amount after some time

Find the yyy-intercept and asymptote

Identify growth or decay and the rate

Write the function from a rate

Find the amount after some time

Find the yyy-intercept and asymptote

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these exponential growth and decay worksheets free?+

Do the exponential growth and decay worksheets come with an answer key?+

Are these exponential growth and decay worksheets printable?+

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Is this a free alternative to Kuta Software for exponential growth and decay?+

Can I choose how hard the exponential growth and decay questions are?+

What kinds of question are on a exponential growth and decay worksheet?+

What do students get wrong with exponential growth and decay?+

Find the $y$ -intercept and asymptote

Find the $y$ -intercept and asymptote