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?

Answer 1

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, $\frac{dB}{dt}=4$