Question

A population is originally 100 individuals, but because of the combined effects of birth and deaths, it tiples each hour.

a. Make a table of the population size for t-0 to 5, where t is measured in hours.

b. Give two equations modeling the population growth by first expressing P[t+1] in terms of Pt] and then expressing AP in terms of Plt)

c. What, if anything, can you say about the birth and death rates for this population?

Answer 1

Explanation:

Given that a population is originally 100 individuals, but because of the combined effects of birth and deaths, it tiples each hour.

a)

t P(t)

0 100

1 300

2 900

3 2700

4 8100

5 24300

6 72900

7 218700

8 656100

9 1968300

10 5904900

b) P(t+1) = 3 P(t)

Generally these form a GP

Hence
`P(t) = 100(3)^(n)`

c) Since population is tripling we say death rate is very small compared to birth rate such that births-deaths = 3 times the existing population.