Question

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^(0.01t) 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. bears show calculator

Explanation:

Step1: Substitute t=25 into the function

$B(25) = 2500 \cdot 2^{0.01 \times 25}$

Step2: Simplify the exponent

$0.01 \times 25 = 0.25$, so $B(25) = 2500 \cdot 2^{0.25}$

Step3: Calculate $2^{0.25}$

$2^{0.25} = \sqrt[4]{2} \approx 1.1892$

Step4: Compute the final population

$B(25) \approx 2500 \times 1.1892$

Answer:

2973 bears