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