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Maurinko [17]
3 years ago
8

A movie theater has been charging $10.00 per person and selling about 500 tickets on a typical weeknight. After surveying their

customers, the theater management estimates that for every 50 cents that they lower the price, the number of moviegoers will increase by 50 per night. Find the demand function. (Let x represent the number of tickets sold and p represent the price.)
Mathematics
1 answer:
kifflom [539]3 years ago
4 0

Answer:

p(x) = -0.01x + 15

Step-by-step explanation:

Given

Let x represent the number of tickets, and p the charges

(x_1,p_1) = (500,10)

A reduction of 50c gives an increment of 50 tickets.

This gives:

(x_2,p_2) = (500+50,10-0,5) ---- 50c = \$0.5

(x_2,p_2) = (550,9.5)

Required

Determine the demand function

First, calculate the slope:

m = \frac{p_2 - p_1}{x_2 - x_1}

m = \frac{9.5 - 10}{550-500}

m = \frac{-0.5}{50}

m = -0.01

So, the equation is:

p = m(x - x_1) + y_1

p = -0.01(x - 500) +10

p = -0.01x + 5 +10

p = -0.01x + 15

Hence, the function is:

p(x) = -0.01x + 15

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Ashley deposits $10 000 at the end of each month for 6 times at rate of 5% compounded monthly. How much will be in her account
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The future values of Ashley's periodic deposits under the five scenarios are stated in the deposit table as follows:

<h3>Deposit Table:</h3>

Item     Initial       Periodic      Deposit    Interest    Future Value    Interest

         Deposit     Deposit        Period        Rate                                    ($)

a.      $10,000     $10,000     6 months        5%        $61,774.51      $1,774.51

b.     $10,000     $10,000     3 months        5%      $30,502.78       $502.78

c.      $10,000    $10,000     6 months        5%        $51,774.51     $1,522.42

d.    $20,000    $10,000      6 months       5%        $72,201.71     $2,201.71

e.   $10,000     $10,000     6 months       5%/6%  $60,803.78       $803.78

<h3>What is the future value?</h3>

The future value of a periodic investment represents the present value of cash flows compounded at an interest rate into the future.

The future value is computed using the FV formula or factor.

It can also be computed using an online finance calculator as follows:

<h3>Data and Calculations:</h3>

Periodic Deposit = $10,000

Investment period = 6 months

Interest rate = 5% compounded monthly

<h3>a) for illustration:</h3>

N (# of periods) = 6 months

I/Y (Interest per year) = 5%

PV (Present Value) = $0

PMT (Periodic Payment) = $10,000

<u>Results</u>:

FV = $61,774.51

Sum of all periodic payments = $60,000 ($10,000 x 6)

Total Interest = $1,774.51

<h3>Other Special Cases:</h3>

c) Interest on $10,000 for 3 months is $1,522.42 ($1,774.51 - $252.09).

d)                             Future Value      Interest

5% with $20,000   $82,285.04    $2,285.04

5% with  $10,000     (10,083.33)          (83.33)

Total for 6 months   $72,201.71     $2,201.71

e)                            Future Value       Interest

5% for 3 months    $30,502.78       $502.78

6% for 3 months     $30,301.00       $301.00

Total for 6 months $60,803.78      $803.78

Learn more about the computation of future values at brainly.com/question/24703884 and brainly.com/question/12979998

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