Problem 4

There is a fertilizer that makes plants grow fast. When you apply this fertilizer, the plant will increase its height by one-half on the first day. On the second day its height increases by one-third of its height of the previous day. On the third day its height increases by one-fourth of its height of the previous day, and so on. How many days does it take to grow to 100 times its original height?

[Problem submitted by Juergen Pahl, LACC Professor of Mathematics.]

Solution for Problem 4:

Let = original height. Then

after one day the height is

after two days the height is

after three days the height is

after four days the height is , etc.

Every day the plant grows by a fixed amount of one half of its original size. Therefore,

after days its height is .

Solution:

days