Question

Let y=20,000(0.95)^x repesents the purchasing power of $20,000 with an inflation rate of 5% per year. The table below represents the first 4 years later, rounded to the nearest dollar. Which year is incorrect?

Years later (x)
Purchasing Power $ (y)
1year =19,100
2years=18,050
3years= 17,148
4years= 16,290

Answer 1

In the given table the purchasing power of first year is incorrect.

Explanation:

The given function is

`y=20000(0.95)^x`

In first year, the purchasing power is

`y=20000(0.95)^(1)=19000`

The purchasing power of first year is incorrect.

In second year, the purchasing power is

`y=20000(0.95)^(2)=18050`

In third year, the purchasing power is

`y=20000(0.95)^(3)=17147.5\approx 17148`

In fourth year, the purchasing power is

`y=20000(0.95)^(4)=16290.125\approx 16290`

Therefore in the given table the purchasing power of 2, 3, and 4 years are correct.

Answer 2

We simply substitute the values of x and check if the values of y match.
y(1) = 19,000
y(2) = 18,050
y(3) = 17,148
y(4) = 16,290

As is visible from the table, the first value quoted is incorrect.