Exponential Growth Math Example 1

Follow the full solution, then compare it with the other examples linked below.

easy

A population of bacteria doubles every

3

hours. If there are initially

500

bacteria, how many will there be after

12

hours?

1
The exponential growth model is $P(t) = P_0 \cdot 2^{t/d}$ , where $d$ is the doubling time.
2
Substitute: $P(12) = 500 \cdot 2^{12/3} = 500 \cdot 2^4$ .
3
$P(12) = 500 \cdot 16 = 8{,}000$ .

Answer

8{,}000 \text{ bacteria}

Exponential growth occurs when a quantity increases by a constant percentage over equal time intervals. The doubling-time formula

P(t) = P_0 \cdot 2^{t/d}

is a special case of

P(t) = P_0 \cdot b^t

. In 12 hours, the population doubles 4 times:

500 \to 1000 \to 2000 \to 4000 \to 8000

About Exponential Growth

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

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