Question

Function Word Problem
The basement of a large department store features discounted merchandise. Their policy is to reduce the previous month's price of the item by 8% each month for 6 months, and then give the unsold items to charity.

Answer 1

i assume you're writing the rest of the question now, haha

Answer 2

Let S6 be the sale price for the sixth month and P the original price. Express S6 as a function of P

Answer 3

Yeah sorry @Omistone

Answer 4

no worries, lemme write this out in my book so i can try to understand it a little clearer.

Answer 5

okay

Answer 6

and then it says What is the final price of a $100 garment on sale for the sixth month?
Round your answer to two decimal places.

Answer 7

ok, so if we let P = the original price, and we know that the price decreases each month by 8% of the previous price, the price for any given month, n, can best be expressed as a geometric progression:
\[S _{n} = P \times 0.92^{n-1} \]
the reason we multiply by 0.92 is because 100% - 8% (for the discount) is 92% (0.92 in decimal form.
so we simply let n = 6
\[S _{6} = P \times 0.904\]

Answer 8

oh, right i didn't see your last post before i posted all that working out, but it should be easy enough for you to round it.

Answer 9

so then , you just substitute in 100 for P in the equation and you will have your answer. I hope this helps, be sure to let me know if you don't understand anything.

Answer 10

I think I understand it. Thank you

Answer 11

S6=P×0.904
= 100 x 0.90
= 90

so the item would be $90 after 6 months

Answer 12

no worries

Answer 13

where does the minus 1 come from in \[0.92^n -1 \] @Omistone

Answer 14

By what total percentage has the garment now been reduced from its original price?
Round your answer to two decimal places.

Answer 15

would the answer to the last one be 10% @Omistone