Problem
Question 8 of 11 , Step 2 of 2 $11 / 15$ Correct 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? Answer Keypad How to enter your answer (opens in new window) Keyboard Shortcuts previous step answer years
Solution
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.
