#### To determine

**To represent:**

What does 100+∫015n'tdt represent.

#### Answer

The total population of honey bees after 15 weeks.

#### Explanation

**1) Concept:**

The Net Change Theorem: The integral of a rate of change is the net change.

∫abF'xdx=Fb-Fa

**2) Given:**

100+∫015n'(t)dt

3) **Calculation:**

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,

∫015n'(t)dt=n15-n(0)

Now substitute the value ∫015n'(t)dt=n15-n(0) in 100+∫015n'tdt.

100+∫015n'tdt=100+n15-n(0)

Substitute n0=100 in above.

100+∫015n'tdt=100+n15-100

Simplify,

100+∫015n'tdt=n15

Thus the integral 100+∫015n'tdt represents thetotal population of the honey bees after 15 weeks

**Conclusion:**

Therefore,100+∫015n'tdt represents thetotal population of the honey bees after 15 weeks.