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HACTEHA [7]
3 years ago
6

Suppose $2000 is deposited in an account paying 2.5% interest compounded quarterly. What will the account balance be after 12 ye

ars?
Mathematics
1 answer:
IrinaVladis [17]3 years ago
6 0
A=p(1+i/m)^mn
A=2000(1+0.025/4)^4*12
A=2,697.2
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A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materi
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The required function is: P(x)=-3x^2+78x-360

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The maximum weekly profit is $147

Step-by-step explanation:

Consider the provided information.

Part (A)

The materials for each feeder cost $6, and the society sells an average of 30 per week at a price of $10 each.

Let x be the price per feeder.

Profit = Revenue - cost

So the profit per feeder is x-6

If we increase then for every dollar increase, it loses 3 sales per week.

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30-3x+30

-3x+60

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P(x)=(x-6)(-3x+60)

P(x)=-3x^2+78x-360

Hence, the required function is: P(x)=-3x^2+78x-360

Part (B) What price should the society charge for each feeder to maximize profits? What is the maximum weekly profit?

The above function is a downward parabola so the maximum will occur at vertex.

The x coordinate of the vertex of parabola is: x=\frac{-b}{2a}

Substitute a=-3, b=78 and c=-360 in above.

x=\frac{-78}{2(-3)}=13

Hence, the price for each feeder to maximize profit should be $13.

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P(x)=-3(13)^2+78(13)-360=$147

Hence, the maximum weekly profit is $147

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