Question

1. Suppose Alice eats 3 ounces of base 2 cake (doubles her height for each ounce eaten) at each meal. a) What will her height be multiplied by after two meals? b) After three meals? c) After four meals? d) After M meals?

Answer 1

a)64

b)512

c)2^12

d)2^3m

Explanation:

At every meal, 3 ounces of the cake is eaten

a) After 2 meals, the number of ounces consumed is 6 ounces

For each ounce, height is doubled , for 6 ounces, we have 2 * 2 * 2 * 2 * 2 * 2

Her height is multiplied by 64

b) After three meals

Total consumption is 3 * 3 = 9 ounces

So her height will be multiplied by 2^9 = 512

c) After four meals

Total ounces is 4 * 3 = 12

So her height will be multiplied by 2^12

d) After M meals

Number of ounces is m * 3 = 3m ounces

Her height will be multiplied by 2^3m