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In a particular region of a national park, there are currently 330 deer, and the population is increasing at an annual rate of 11%.
Write an exponential function to model the deer population.
Explain what each value in the model represents.
Predict the number of deer that will be in the region after five years. Show your work.
The exponential function to model the deer population can be written as:
P(t) = 330 * 1.11^t
Where:
- P(t) is the deer population after t years
- 330 is the initial deer population
- 1.11 is the growth factor representing an annual increase of 11%
- t is the number of years
To predict the number of deer in the region after five years, we substitute t = 5 into the exponential function:
P(5) = 330 * 1.11^5
P(5) = 330 * 1.767161
P(5) ≈ 584.47
Therefore, the predicted number of deer in the region after five years is approximately 584.