Question 8 of 11 , Step 2 of 2
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A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to $\mathrm{P}(\mathrm{t})=(167) 3^{\frac{1}{4}}$, where $t$ represents the number of years from the time of introduction.
Step 2 of 2 : How long will it take for the population to reach 4509 deer, according to this model?
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Final Answer: The time it will take for the population to reach 4509 deer according to this model is \(\boxed{12}\) years.
Step 1 ：The question is asking for the time it will take for the population of deer to reach 4509 according to the model \(P(t) = 167 * 3^{(t/4)}\).
Step 2 ：To solve this, we need to set \(P(t)\) equal to 4509 and solve for t. This will involve using logarithms to solve for t.
Step 3 ：Let's set up the equation: \(4509 = 167 * 3^{(t/4)}\)
Step 4 ：Solving this equation gives us \(t = 12.0\)
Step 5 ：Final Answer: The time it will take for the population to reach 4509 deer according to this model is \(\boxed{12}\) years.
