Question

11. The doubling time of a population of plants is 12 years. Assuming that the initial population is 300 and that the rate of increase remains constant, how large will the population be in 36 years

Answer 1

Answer:

The population will be of 2400 in 36 years.

Step-by-step explanation:

The equation for the population of plants after t years follows the following format:

$P(t) = P(0)(1+r)^{t}$

In which P(0) is the initial amount of plants and r is the yearly rate which it increases.

Assuming that the initial population is 300

This means that P(0) = 300.

The doubling time of a population of plants is 12 years.

This means that P(12) = 2*300 = 600.

We use this to find r.

$P(t) = P(0)(1+r)^{t}$

$600 = 300(1+r)^{t}$

$(1+r)^{12} = 2$

$\sqrt[12]{(1+r)^{12})} = \sqrt[12]{2}$

$1 + r = 1.05946$

So

$P(t) = 300(1.05946)^{t}$

How large will the population be in 36 years

This is P(36)

$P(t) = 300(1.05946)^{36} = 2400$

The population will be of 2400 in 36 years.