How long before one plant becomes 20?

Question

1 plant will populate into 20 before the original dies of age.

Measurement of time starts at the beginning of the original plants growth cycle.

The growth cycle of each plant is 3 time units to reach full maturity.

Upon reaching full maturity each plant will expend 1 time unit to produce and drop a single seed which will become the growth cycle of a new plant.

Each new plant will continue to sprout and drop seeds at one time unit intervals until a population of 20 mature plants is achieved.

Answer 1

The original seed is planted at time zer0

After three units of time it matures

After 1 unit of time, it reproduces

After 1 unit of time, it reproduces again while the 2nd matures

After 1 unit of time, it reproduces again while the 2nd matures

After 1 unit of time there are now 2 mature, while another baby seed is reproduces

At this time, there are 2 matures and 3 babies.

Moving forward, another will mature while the matures will continue to reproduce.

Therefore after 25 time units, there will be 20 mature plants and the original will die.

I created a table in excel that verifies this. I gave up on the back-log of baby seeds, but

it does not get through the first generation of the alphabet before the original seed dies.

The file name is seeds.xls has is posted in the RESOURCE section under toolkit.