An electronics store has two options for liquidating televisions that have not sold.

Option 1: decrease the price of each television by 5% each month

Option 2: decrease the price of each television by $30 each month

Which function shows the difference in price between option 1 and option 2 for a television that originally costs $350, where x is the number of months since the price decreases began?

350 (0.95) ^x + 30x - 350

350 (0.95) ^x - 30x - 350

350 (1.5) ^x - 30x + 350

350 (0.5) ^x + 30x - 350

Answser: first option 350 (0.95) ^x + 30x - 350

Explanation:

You can figure out the function that shows the difference in price between option 1 and option 2 if you make a table simulating the behavior for a few months:

month price as per option 1 price as per option 2

start 350 350

1 350 - 5% (350) = 350 - 30

= 350 (0,95)

2 350 (0,95) * (0,95) =

350 (0,95) ² 350 - 30 (2)

3 350 (0,95) ³ 350 - 30 (3)

So now you can figure out the price with each option after x months:

350 (0.95) ˣ 350 - 30x

And the difference is 350 (0.95) ˣ - [350 - 30x]

Which, expanding the square brackets, is 350 (0.95) ˣ + 30x - 350 ↔ the first option.