** **

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