Let the insect population be .

(a)

If the insect population increases by a constant amount  every month.

Apply integral on each side.

.

Therefore, the population grows linearly.

(b)

If the insect population increases by a constant percentage every month.

Apply integral on each side.

Apply exponent on each side.

.

Therefore, the population grows exponentially.

(a) , the population grows linearly.

(b) , the population grows exponentially.