Practice Exponential Growth in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Exponential growth occurs when a quantity increases by a constant multiplicative factor over equal intervals.

Exponential growth means the amount added each period is proportional to the current amount — the bigger it gets, the faster it grows, creating an accelerating curve.

Showing a random 20 of 50 problems.

Example 1

medium
A quantity grows from 5050 to 200200 over two equal steps. Find the constant multiplier.

Example 2

medium
A YouTube channel grows from 10001000 to 60006000 subscribers in 44 years. Assuming exponential growth, find the annual growth rate.

Example 3

medium
An investment of $1000\$1000 grows 10%10\% per year. Find its value after 22 years.

Example 4

easy
Is y=9⋅(0.85)xy = 9 \cdot (0.85)^x growth or decay?

Example 5

easy
Evaluate y=6⋅2xy = 6 \cdot 2^x at x=4x = 4.

Example 6

medium
Solve 5⋅3x=4055 \cdot 3^x = 405 for xx.

Example 7

easy
Evaluate y=3⋅2xy = 3\cdot 2^x at x=0x = 0.

Example 8

challenge
A starting population of 11 doubles every minute and fills a jar at minute 6060. At what minute is the jar half full?

Example 9

easy
A population doubles each year starting at 100100. Write its model.

Example 10

easy
What is the initial value of y=8⋅1.2xy = 8\cdot 1.2^x?

Example 11

medium
Compare y=2xy = 2x and y=2xy = 2^x at x=10x = 10.

Example 12

easy
Is y=4⋅3xy = 4\cdot 3^x growth or decay?

Example 13

easy
A quantity grows at 8%8\% per year. What is the growth factor bb?

Example 14

easy
What is the initial value of y=12⋅1.08xy = 12 \cdot 1.08^x?

Example 15

medium
An investment grows from $1,000\$1{,}000 to $1,500\$1{,}500 in 55 years with continuous compounding. Find the annual growth rate.

Example 16

challenge
Two accounts start at $1000\$1000: one earns $100\$100 per year (simple), one earns 10%10\% per year (compound). After 2 years, which is larger and by how much?

Example 17

hard
A bank account earns 4%4\% compounded quarterly. Find the effective annual rate.

Example 18

medium
$2000 is invested at 5%5\% compounded annually. What is the balance after 88 years?

Example 19

medium
A city's population grows at 3%3\% per year. If the current population is 200,000200{,}000, when will it reach 300,000300{,}000?

Example 20

hard
A population grows continuously according to P(t)=P0e0.04tP(t) = P_0 e^{0.04 t}. How long until the population triples?
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