The new iPhone 3.14 is being sold at the UT Math Department. The original price is $1100 (day 0), but they are going to decrease the price of the phone by x percent each day. You decided to wait until the price dropped to $67.59 on the 16th day to purchase yours.
What was the daily percent decrease that the UT Math Department set for the iPhone 3.14?
A = Accumulated amount = 67.59
P = Initial amount = 1100
r = rate
t = elepsed time = 16
A = P ( 1 - r )ᵗ
67.59 = 1100 ( 1 - r )¹⁶
67.59 / 1100 = ( 1 - r )¹⁶
¹⁶√ ( 67.59 / 1100 ) = 1 - r
r = 1 - ¹⁶√ ( 67.59 / 1100 )
r = 1 - 0.84
r = 0.16
r = 0.16 ∙ 100%
r = 16%
holy smoke! How outdated is your vocabulary
Well, it seems like the UT Math Department really knows how to calculate discounts! Let's do some math together, just for fun.
First, let's figure out the total discount from the original price to the final price. The original price is $1100, and the final price is $67.59. So the discount is $1100 - $67.59 = $1032.41.
Now, let's calculate the daily percent decrease. Since the price was decreasing each day, we can divide the total discount by the number of days it took to reach the final price. The total discount is $1032.41, and it took 16 days to reach the final price. So the daily percent decrease is $1032.41/16 = $64.525625.
Oh wait, that's a dollar value! Let me recalculate that as a percentage. So, the daily percent decrease is approximately 64.53 percent.
Wow, that's quite a discount! The UT Math Department really knows how to subtract some dollars and cents. I hope this math lesson was entertaining for you!
To determine the daily percentage decrease, we can utilize the initial price and the final price on the 16th day.
First, let's calculate the total decrease in price over the 16 days by subtracting the final price from the initial price:
Total price decrease = Initial price - Final price = $1100 - $67.59 = $1032.41.
Next, we divide the total price decrease by the number of days (16) to find the daily decrease:
Daily decrease = Total price decrease / Number of days = $1032.41 / 16 = $64.53.
Lastly, to calculate the daily percentage decrease, we divide the daily decrease by the initial price and multiply by 100:
Daily percentage decrease = (Daily decrease / Initial price) * 100 = ($64.53 / $1100) * 100 ≈ 5.87%.
Therefore, the daily percent decrease set by the UT Math Department for the iPhone 3.14 is approximately 5.87%.
Holy smoke! How outdated is that question?? iPhones are up to XR, XS, 11, and 11 Pro. Be sure to ask your teacher why such outdated info is being used. This is like asking about Windows Vista instead of Windows 10!
The math is a good exercise. Please wait for a math tutor to come online.