For each year t, the number of trees in Forest A is represented by the function A(t) = 72(1.025). In a neighboring forest, the number of tre

Question

For each year t, the number of trees in Forest A is represented by the function A(t) = 72(1.025). In a neighboring forest, the number of trees in Forest B is represented by the function B(t) = 63(1.029).

Assuming the population growth models continue to represent the growth of the forests, which forest will have a greater number of trees after 20 years? By how many?

Round your answer to the nearest tree.

Forest A or B will have _________ more trees.​

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Minh Khuê 3 years 2021-07-20T21:59:47+00:00 1 Answers 81 views 0

Answers ( )

  1. diemkieu
    0
    2021-07-20T22:00:56+00:00
    Reply

    Answer:

    Forest A will have 6 more trees.

    Step-by-step explanation:

    The number of trees in Forest A is represented by the function:

    A(t)=72(1.025)^t

    And Forest B is represented by:

    B(t)=63(1.029)^t

    And we want to determine which forest will have the greater number of trees after 20 years.

    So, evaluate both functions for t = 20. For Forest A:

    \displaystyle \begin{aligned} A(20)&=72(1.025)^{20} \\ &=117.9803...\\ &\approx 118 \text{ trees} \end{aligned}

    And for Forest B:

    \displaystyle \begin{aligned} B(20) &= 63(1.029)^{20} \\ &=111.5958... \\ &\approx 112 \end{aligned}

    Therefore, after 20 years, Forest A will have 6 more trees.

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