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A breeding group of beavers is introduced into a protected area. After t years the number of beavers in the area is modeled by the function


N(t)= 54/0.35+0.68^t

  1. How many beavers were initially introduced?
  2. Estimate the number of beavers after 5 years.
  3. Determine the change in the beaver population between t = 5 and t = 10.

(Note: All answers are whole numbers.)

Verified Answer :

LammettHash

\(N(t)=\dfrac{54}{0.35+0.68^t}\)

The number of beavers initially introduced is the population at time \(t=0\), so you need to find \(N(0)\).

\(N(0)=\dfrac{54}{0.35+0.68^0}=\dfrac{54}{1.35}=40\)

The number of beavers after 5 years is given by \(N(5)\).

\(N(5)=\dfrac{54}{0.35+0.68^5}\approx\dfrac{54}{0.495}\approx109\)

The change in the beaver population between \(t=5\) and \(t=10\) is simply the difference \(N(10)-N(5)\). Evaluate the function at these points (you already know \(N(5)\)) and subtract. You should get approximately \(36.49\approx36\).

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