Question

By what factor does the population grow every 2 years? Use rhis information to fill out the table.By what factor does the population grow every year? explain how you know, and use this information to complete the table.

Answer 1

From the table, we see that:

• Year 0 has a population of 10,

,

• Year 2 has a population of 20.

So after two years, the population of fish is doubled.

1) By year 4, we will have double the population of year 2, so the population will be 2*20 = 40.

2) To function that describes the growth of the population is:

`P(t)=P_0\cdot r^t._{}`

Where P_0 is the initial population and r is the growth factor.

We know that after two years, the population of fish is doubled:

`P(t+2)=2\cdot P(t)\text{.}`

Using the formula above evaluated in t + 2, we have:

`P(t+2)=P_0\cdot r^(t+2)=(P_0\cdot r^t)\cdot r^2=P(t)\cdot r^2`

Equalling the last two equations, we have:

`P(t+2)=2\cdot P(t)=P(t)\cdot r^2\text{.}`

Solving for r the last equation, we have:

`\begin{gathered} 2=r^2, \\ r=\sqrt[]{2}\text{.} \end{gathered}`

So the growth factor is r = √2.

Answer:

1. 40

2. √2