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Enzo is studying the black bear population at a large national park.
He finds that the relationship between the elapsed time 
t, in years, since the beginning of the study, and the black bear population 
B(t), in the park is modeled by the following function.

B(t)=2500*2^(0.01 t)
According to the model, what will the black bear population be at that national park in 25 years?
Round your answer, if necessary, to the nearest whole number.

Enzo is studying the black bear population at a large national park.\newlineHe finds that the relationship between the elapsed time t t , in years, since the beginning of the study, and the black bear population B(t) B(t) , in the park is modeled by the following function.\newlineB(t)=250020.01t B(t)=2500 \cdot 2^{0.01 t} \newlineAccording to the model, what will the black bear population be at that national park in 2525 years?\newlineRound your answer, if necessary, to the nearest whole number.

Full solution

Q. Enzo is studying the black bear population at a large national park.\newlineHe finds that the relationship between the elapsed time t t , in years, since the beginning of the study, and the black bear population B(t) B(t) , in the park is modeled by the following function.\newlineB(t)=250020.01t B(t)=2500 \cdot 2^{0.01 t} \newlineAccording to the model, what will the black bear population be at that national park in 2525 years?\newlineRound your answer, if necessary, to the nearest whole number.
  1. Identify Function and Value: Identify the function and the value of tt to use.\newlineWe have the function B(t)=2500×20.01tB(t) = 2500 \times 2^{0.01t}. We need to find B(25)B(25) since t=25t = 25 years.
  2. Substitute t=25t = 25: Substitute t=25t = 25 into the function.\newlineB(25)=2500×20.01×25B(25) = 2500 \times 2^{0.01 \times 25}
  3. Calculate 0.01×250.01 \times 25: Calculate 0.01×250.01 \times 25.\newline0.01×25=0.250.01 \times 25 = 0.25
  4. Calculate 20.252^{0.25}: Calculate 20.252^{0.25}.20.251.18922^{0.25} \approx 1.1892
  5. Multiply by 11.18921892: Multiply 25002500 by 1.18921.1892.\newline2500×1.189229732500 \times 1.1892 \approx 2973

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