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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.
bears

Enzo is studying the black bear population at a large national park. $\newline$ 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. $\newline$ $B(t)=2500 \cdot 2^{0.01 t}$ $\newline$ 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. $\newline$ bears

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Compound interest: word problems

Full solution

Q. Enzo is studying the black bear population at a large national park.

\newline

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.

\newline

B(t)=2500 \cdot 2^{0.01 t}

\newline

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.

\newline

bears

Identify values and function: Identify the values of $t$ and the function $B(t)$ . $\newline$ Elapsed time ( $t$ ) = $25$ years $\newline$ The function that models the black bear population is $B(t) =$ $2500$ \times $2$ ^{( $0$ . $01$ t)}.
Substitute value into function: Substitute the value of $t$ into the function $B(t)$ . $\newline$ $B(25) = 2500 \times 2^{(0.01 \times 25)}$
Calculate the exponent: Calculate the exponent. $\newline$ $0.01 \times 25 = 0.25$
Calculate $2$ raised to the power: Calculate $2^{0.25}$ . $\newline$ $2^{0.25} \approx 1.189207115$
Multiply result by $2500$ : Multiply the result by $2500$ to find $B(25)$ . $\newline$ $B(25) = 2500 \times 1.189207115$ $\newline$ $B(25) \approx 2973.0177875$
Round result to nearest whole number: Round the result to the nearest whole number. $B(25) \approx 2973$ bears

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