40 bacteria triple each hour. Write the model. Step by Step

Step by step

The question

Question: 40 bacteria triple each hour.

Write the model.

1 Find the start

t is the time in hours.

We call the number N.

N = number, t = hours

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

Then the number is 40.

That is the start.

start, t = 0: N = 40

2 Find the factor

To triple means three times as much: times 3.

triple = × 3

So the factor is 3: each hour, we multiply by 3.

factor: × 3 each hour

3 Make a small table

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

Each step, we multiply by 3: 40 times 3 is 120.

Times 3 again is 360.

After 2 hours, we multiplied by 3 two times.

Two times is the power 2: 3 squared.

t = 2: 40 × 3 × 3 = 40 × 3²

After t hours, we multiply t times.

So the power is t.

after t hours: × 3, t times = × 3^t

4 Write the model

Start times the factor, to the power t.

So the model is N = 40 times 3 to the power t.

N = 40 × 3^t

5 Check

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

3 to the power 3 is 27.

40 times 27 is 1080.

model, t = 3: 40 × 3³ = 40 × 27 = 1080

One more step of the table: 360 times 3 is 1080 too.

It works!

table, one more step: 360 × 3 = 1080

Let's look back.

First: find the start.

Then: find the factor.

Then: make a small table.

Then: write the model.

Last: check.

Answer