300 rabbits double each year. Write the model. Step by Step

Step by step

The question

Question: 300 rabbits double each year.

Write the model.

1 Find the start

t is the time in years.

We call the number N.

N = number, t = years

At the start no time has passed: t = 0.

Then the number is 300.

That is the start.

start, t = 0: N = 300

2 Find the factor

To double means two times as much: times 2.

double = × 2

So the factor is 2: each year, we multiply by 2.

factor: × 2 each year

3 Make a small table

A small table: t = 0, 1, 2.

Each step, we multiply by 2: 300 times 2 is 600.

Times 2 again is 1200.

After 2 years, we multiplied by 2 two times.

Two times is the power 2: 2 squared.

t = 2: 300 × 2 × 2 = 300 × 2²

After t years, we multiply t times.

So the power is t.

after t years: × 2, t times = × 2^t

4 Write the model

Start times the factor, to the power t.

So the model is N = 300 times 2 to the power t.

N = 300 × 2^t

5 Check

Let's check one more step, t = 3.

2 to the power 3 is 8.

300 times 8 is 2400.

model, t = 3: 300 × 2³ = 300 × 8 = 2400

One more step of the table: 1200 times 2 is 2400 too.

It works!

table, one more step: 1200 × 2 = 2400

Let's look back.

First: find the start.

Then: find the factor.

Then: make a small table.

Then: write the model.

Last: check.

Answer