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ratelena [41]
3 years ago
14

A movie theater charges $5 per ticket and averages 300 customers each night. If prices are raised to $7 per ticket, the theater

estimates that average nightly ticket sales will be $1,750. What is the percentage change in the average number of customers the theater has each night? (Express your answer in whole numbers; round decimals up or down).
Mathematics
1 answer:
Shtirlitz [24]3 years ago
4 0

Attendance with the higher ticket price is ...

... $1750/$7 = 250

So the percentage change in attendance is ...

... change = (new - original)/original × 100%

... = (250 -300)/300 × 100% = -1/6×100% ≈ -17%

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Correct answers are:
(1) <span>28, 141 known cases
(2) 79913.71 known cases after six weeks (round off according to the options given)
(3) After approx. 9 weeks (9.0142 in decimal)

Explanations:
(1) Put x = 0 in given equation
</span><span>y= 28, 141 (1.19)^x
</span><span>y= 28, 141 (1.19)^(0)
</span>y= 28, 141


(2) Put x = 6 in the given equation:
<span>y= 28, 141 (1.19)^x
</span><span>y= 28, 141 (1.19)^(6)
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(3) Since
y= 28, 141 (1.19)^x
And y = <span>135,000

</span>135,000 = 28, 141 (1.19)^x
135,000/28, 141 = (1.19)^x

taking "ln" on both sides:
ln(4.797) = ln(1.19)^x

ln(4.797) = xln(1.19)
x = 9.0142 (in weeks)

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