Question

answer these questions to 4 digits past the decimal place. DO NOT include units in your answer.People often underestimates the effects of slight changes when they occur over long periods of time. Imagine a population with a mean body length of 1.0 meters. If the population increases its average length by 0.01% per generation(compared to each generation's previous mean length), what will the new mean length be after each of the following lengths of time:

Over 50 generations?

Over 1,000 generations?

Over 10,000 generations?

Over 100,000 generations?

Please show the math and explain how you did this?

Answer 1

Mean body length An after n generations is given by:

where

An = Mean body length after n generations (to be found)

P = Initial Mean body length = 1.0

r = Rate of increase = 0.01/100 = 0.0001

Substituting, we get:

(i)

For n = 50, we get:

(ii)

For n = 1000, we get:

(iii)

For n = 10000, we get:

(iv)

For n = 100000, we get:

So,

Answers are:

Over 50 generations: 1.0050

Over 1,000 generations: 1.1052

Over 10,000 generations: 2.7181

Over 100,000 generations: 22015.4560