(e) The number of bees spotted in Amelie’s garden can also be modeled by the function B(x) = 50√ k + 2x where x is the daily high temperatur

Question

(e) The number of bees spotted in Amelie’s garden can also be modeled by the function B(x) = 50√ k + 2x where x is the daily high temperature, in degrees Fahrenheit, and k is a positive constant. When the number of bees spotted is 100, the daily high temperature is increasing at a rate of 2 ◦F per day. According to this model, how quickly is the number of bees changing with respect to time when 100 bees are spotted?

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Allison 3 days 2021-10-09T19:58:45+00:00 1 Answer 0

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    2021-10-09T20:00:16+00:00

    Answer:

    \frac{dB}{dt}=4

    Step-by-step explanation:

    Derivative indicates rate of change of dependent variable with respect to independent variables. It indicates the slope of a line that is tangent to the curve at the specific point.

    Given:

    Number of bees is modeled by the function B(x)=50\sqrt{k}+2x

    The daily high temperature is increasing at a rate of 2 °F per day when  the number of bees spotted is 100.

    To find:

    rate of change of number of bees when 100 bees are spotted

    Solution:

    B(x)=50\sqrt{k}+2x

    Differentiate with respect to t,

    \frac{dB}{dt}=0+2(\frac{dx}{dt}) \\\frac{dB}{dt}=2(\frac{dx}{dt}) \\

    Put (\frac{dx}{dt}) =2

    \frac{dB}{dt}=2(2)=4

    At x = 100, \frac{dB}{dt}=4

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