Answer

After one bite, half the cookie remains. After two bites, one-fourth of the cookie remains. With each bite, the remaining portion of cookie gets halved. Let's put this information in a table:

After the n^th bite, the fraction of cookie remaining is .

(a) After 5 bites, the fraction of cookie remaining is

This means Cookie Monster has eaten  of the cookie.

(b) We want to find the first value of n for which

Since , we need to solve the inequality

Multiplying both sides by 2ⁿ and by 1000, we have

1000 < 2ⁿ

log ₂ 1000 < n

9.966 < n

In order for n to be a whole number greater than 9.966, we must have n = 10. To make sure, we can check the values of a₉ and a₁₀.

It takes 10 bites before less than one one-thousandth of the cookie remains.