Question: Question 11 of 12, Step 1 of 2 12/16 Correct A certain species of deer is to be introduced into a…

Question 11 of 12, Step 1 of 2

12/16 Correct

A certain species of deer is to be introduced into a forest, and wildlife experts estimate the population will grow to \( P(t) = (759)3^{\frac{t}{2}} \), where \( t \) represents the number of years from the time of introduction.

Step 1 of 2: What is the tripling-time for this population of deer?

Answer

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years

Solution

To find the tripling time for the population of deer, we have the function \( P(t) = 759 \cdot 3^{t/2} \). We need to determine when the population triples. This means we set \( P(t) = 3 \times 759 \). Start with the equation: \[ 3 \times 759 = 759 \cdot 3^{t/2} \] Divide both sides by 759: \[ 3 = 3^{t/2} \] Since the bases are the same, equate the exponents: \[ 1 = \frac{t}{2} \] Multiply both sides by 2 to solve for \( t \): \[ t = 2 \] So, the tripling-time is 2 years.