Exponential Growth
In short: Exponential growth is what happens when a quantity rises by one fixed percent per period, so every period adds more than the one before.
Algebra 1Functions and GraphsF-LE.A.1c
What is Exponential Growth?
A town gaining 4% of its people each year adds more residents every year than the year before, because 4% of a bigger crowd is bigger, and this snowballing pattern is exponential growth.
The model is \(A = P(1 + r)^t\), with starting amount \(P\), rate \(r\) as a decimal, \(t\) periods, and growth factor \(1 + r\). Any factor above 1 yields a curve that crawls at first and then climbs very steeply.
How to spot it
- A quantity rises by a percent per day, month or year rather than by a fixed amount.
- Wording like doubles every, triples each, grows 6% per year or increases by a factor of appears.
- A table shows outputs multiplying by the same number between equal time steps.
- A graph starts low and then climbs ever more quickly.
The method
- Turn the percent into a decimal and add 1, so 4% becomes the growth factor 1.04.
- Name the starting amount P and the count of periods t.
- Place the numbers in \(A = P(1 + r)^t\) to model the exponential growth.
- Handle the power before the multiplication, and round only in the last line.
Exponential Growth: solved example
Problem
A Georgia town of 12,000 residents expands by 4% every year. Predict the head count six years out, rounded to a whole person.
Solution
The growth factor is \(1 + 0.04 = 1.04\). Use \(A = 12{,}000(1.04)^6\).
\(1.04^6 \approx 1.265319\), so \(A \approx 12{,}000 \times 1.265319 \approx 15{,}183.8\). The town will have about 15,184 residents.
Try it
Question 1
A $250 account grows 10% per year. How much is there after 3 years?
Show the answer
\(250(1.1)^3 = 250(1.331) = 332.75\), so $332.75.
Question 2
What is the growth factor for a 12% increase per period?
Show the answer
\(1 + 0.12 = 1.12\).
Exponential Growth vs. Exponential Decay
The two share one type of function, and the factor decides direction: above 1 the amount climbs, between 0 and 1 it falls. A 4% rise has factor 1.04 and a 4% drop has factor 0.96, so check which side of 1 you are on before computing exponential growth.
Keep going
Lessons
Worksheets and quizzes
Related words
- Exponential Function
- Exponential Decay
- Compound Interest
- Percent Increase
- Geometric Sequence
- Linear Function
Whole dictionary: A–Z · Algebra 1 · Functions and Graphs