Answer:
[tex]\frac{dB}{dt}=4[/tex]
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 [tex]B(x)=50\sqrt{k}+2x[/tex]
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:
[tex]B(x)=50\sqrt{k}+2x[/tex]
Differentiate with respect to t,
[tex]\frac{dB}{dt}=0+2(\frac{dx}{dt}) \\\frac{dB}{dt}=2(\frac{dx}{dt}) \\[/tex]
Put [tex](\frac{dx}{dt}) =2[/tex]
[tex]\frac{dB}{dt}=2(2)=4[/tex]
At x = 100, [tex]\frac{dB}{dt}=4[/tex]
