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FrozenT [24]
3 years ago
8

Help please and Thank you!

Mathematics
1 answer:
Cloud [144]3 years ago
8 0

Answer:

Dat boi owes $6,016.17

Step-by-step explanation:

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Student council expects $150 students for a dance and spends $10 on food for each student. The council expects the number of stu
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Answer:

A) S(t)=150(1.08)^{t-1} B) A(t)=10(0.96)^{t-1}

C) If\:t = 1\\E(t)=150\times10\\ \\If\:t >1\\E(t)=150(1.08)^{t-1}\times10(0.96)^{t-1}

Step-by-step explanation:

Considering that The Student Council expects to 150 students for a dance, and spends $10 per student.

If the expectancy is that the number of students increases by  8%

Then since the growth is 8%

we can write the the Predicted Number of Students as a Geometric Sequence,

A.

a_{1}=150\\a_{2}=150\times 1.08 =162\\a_{3}=162\times 1.08= 174.96\approx 175\\a_{4}=175\times1.08=189\\a_{5}=189\times 1.08=204.12\approx 204\\

Therefore,

S(t)=150(1.08)^{t-1}

B) If we spend $10 per student on the 1st year, but the Council wants to reduce the expenditure 4% yearly. Since we want to reduce 4% we must multiply by 96%.

b_{1}=10\\b_{2}=10*(0.96)=9.6\\b_{3}=9.6*(0.96)=9.22\\b_{4}=9.22*(0.96)=8.85\\b_{5}=8.85*(0.96)=8.50

Therefore we can write:

A(t)=10(0.96)^{t-1}

C)

The total expenditure for food must be reduced, by 4%. As long as the public goes increasing by 8% yearly this

So,

If\:t = 1\\E(t)=150\times10\\ \\If\:t >1\\E(t)=150(1.08)^{t-1}\times10(0.96)^{t-1}

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Your final answer will be B) 8 qts
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