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.

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