A phone is worth $900 and loses 20% of its value each year. Write… Step by Step

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The question

Question: A phone is worth $900 and loses 20% of its value each year.

Write the model.

1 Find the start

t is the time in years.

We call the value V.

V = value, t = years

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

Then the value is $900.

That is the start.

start, t = 0: V = $900

2 Find the factor

Each year, 20% of the value is lost.

What is left is 100% take away 20%: 80%.

100% − 20% = 80%

Percent means out of 100.

So 80% is 80/100: 0.8.

80% = 80100 = 0.8

So the factor is 0.8: each year, we multiply by 0.8.

factor: × 0.8 each year

3 Make a small table

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

Each step, we multiply by 0.8: 900 times 0.8 is 720.

Times 0.8 again is 576.

After 2 years, we multiplied by 0.8 two times.

Two times is the power 2: 0.8 squared.

t = 2: 900 × 0.8 × 0.8 = 900 × 0.8²

After t years, we multiply t times.

So the power is t.

after t years: × 0.8, t times = × 0.8^t

4 Write the model

Start times the factor, to the power t.

So the model is V = 900 times 0.8 to the power t.

V = 900 × 0.8^t

Careful!

Not 0.2.

That is the part that is lost.

We multiply by the part that is left: 0.8.

Careful: not V = 900 × 0.2^t ✗

5 Check

Let's check the first year the story way.

20% of 900 is 0.2 times 900: 180.

20% of 900 = 0.2 × 900 = 180

It loses 180: 900 minus 180 is 720.

900 − 180 = 720

The model at t = 1 gives 900 times 0.8: 720 too.

It works!

model, t = 1: 900 × 0.8¹ = 720

Let's look back.

First: find the start.

Then: find the factor.

Then: make a small table.

Then: write the model.

Last: check.

Answer