What does 100+∫015n'tdt represent.
The total population of honey bees after 15 weeks.
The Net Change Theorem: The integral of a rate of change is the net change.
Consider the integral,
100+∫015n'tdt, where n't represents the rate of increasing honey bees per week and starts with 100 honey bees’ i.e. n0=100
By using the net change theorem,
Now substitute the value ∫015n'(t)dt=n15-n(0) in 100+∫015n'tdt.
Substitute n0=100 in above.
Thus the integral 100+∫015n'tdt represents thetotal population of the honey bees after 15 weeks
Therefore,100+∫015n'tdt represents thetotal population of the honey bees after 15 weeks.