Question

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?

Answer 1

The decrement in the price of iPhone is an illustration of geometric progression.

The daily percentage decrease is 17%

The initial price is given as:

$\mathbf{a =1100}$

The common ratio is given as:

$\mathbf{r = x\%}$

The price on the 16th day is:

$\mathbf{a_{16} = 67.59}$

The nth term of a GP is:

$\mathbf{a_n = ar^{n-1}}$

So, we have:

$\mathbf{67.59= 1100 \times x^{16-1}}$

Divide both sides by 1100

$\mathbf{0.06144545454= x^{16-1}}$

This gives

$\mathbf{0.06144545454= x^{15}}$

Take 15th root of both sides

$\mathbf{0.83029= x}$

Rewrite as:

$\mathbf{x = 0.83029}$

Express as percentage

$\mathbf{x = 83.029\%}$

Approximate

$\mathbf{x = 83.0\%}$

Subtract 83% from 1

$\mathbf{Daily = 1 -83\%}$

$\mathbf{Daily = 17\%}$

Hence, the daily percentage decrease is 17%

Read more about geometric sequence at:

https://brainly.com/question/22445557