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# Population Growth

Population Growth. Logistic and Exponential Growth Problems. 2 Types:. Exponential Growth Population increases rapidly (resources unlimited) r &gt; 0 Is the sky the limit? Logistic Growth Happens after exponential growth Population will reach a carry capacity (K) or crash.

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## Population Growth

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1. Population Growth Logistic and Exponential Growth Problems

2. 2 Types: • Exponential Growth • Population increases rapidly (resources unlimited) • r > 0 • Is the sky the limit? • Logistic Growth • Happens after exponential growth • Population will reach a carry capacity (K) or crash

3. Exponential Growth • N = population size (changes through time) • r = growth rate (factor by which population increases) • r = _________ • Formula: dN/dt = rN

4. Exponential Growth Example

5. Exponential Growth • What if you wanted to figure out the population of the rabbits after 30 years? • Darwin said exponential growth can’t last forever . . . leads to . . .

6. Logistic Growth • K = carrying capacity (max amount in a population that the ecosystem can support) • Why? Limited resources/limiting factors  slow population growth • dN/dt = change in the population size over time • FORMULA: dN/dt = rN(K-N/K)

7. Examples: • Take a quick look at how a rabbit population would grow exponentially…

8. Exponential GrowthHow many years does it take to reach K? Recall: dN/dt = rN(K-N/K)

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