Cherub Ruiz
Maple Lab #2
1. Bacteria Count. The number of bacteria in a refrigerated food is N(T). Where T is the
temperature of the food in degrees Celsius. When the food is removed from the refrigerator the
temperature is T (t), where t is the time in hours.
(a) The formula for the composite N (T(t)). What does this function represent? Explain.
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The graph shows that as t increases after two hours the rate of bacteria increased after been
removed from the refrigerator. Therefore, when the temperature increase the rate of bacteria
increased. The lower the temperature the less bacteria present.
(C) The number of bacteria in the food when t = 2 hours.
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The number of bacteria in the food when t = 2 hours is 1700. The total more than double in one
hour.
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(d) The time when the bacterial count reaches 2000.
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2. A sidewalk espresso stand finds that the weekly profit for their businessis a function of the
price they charge per cup. If x equals the price (in dollars) of one cup, the weekly profit is given
by P(x).
(a) What is the maximum profit?
Maximize(s(t),t=0.4..0.6,location);
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When the price is equal to 5/4 or $1.25 the maximum profit is 6525/4 or $1631.25.
(b) Which function, p (x-2) or p(x)-2, gives a fuction that has the same maximum profit? Explain
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(c) What price per cup produces that maximum profit?
The maximum profits equals to $1.25 per cup.
(d) Which fuction, p(x+50) or p(x)+50, gives a function where the price per cup (that produced
the maximum profit) remains unchanged? Explain
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3. Fencing a Garden. A gardener has 140 feet of fencing to fence a rectangular vegetable garden.
(a) Find a function that models the area of the garden she can fence and write it in maple form.
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The maximum area that can be reached is 1225 ft^2; therefore, the she will be unable to fence a
garden with 1250ft^2.
(e) Find the dimensions of the largest area she can fence.
The largest area she can fence is when L = 35 and the area is 1225ft^2.
4.
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