Question 142450This question is from textbook Mathematical Ideas
: I am having problems trying to figure out what variable I have to solve for in these two problems. Could anyone please help me with these? Thank you so much!
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2. Assume the cost of a company picnic is described by the function
P(n) = (1/2)n2 – 10n + 80
Where n represents the number of employees and family members attending the picnic and P (in dollars) represents the cost of the picnic. How many employees and guests in attendance produce a minimum cost? What is the minimum cost for this event?
3. In the formula N = Iekt, N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. There are currently 45 million cars in a certain country, increasing by 3.2% annually. How many years will it take for this country to have 61 million cars. Round to the nearest year.
This question is from textbook Mathematical Ideas
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 2. Assume the cost of a company picnic is described by the function
P(n) = (1/2)n^2 – 10n + 80
Where n represents the number of employees and family members attending the picnic and P (in dollars) represents the cost of the picnic. How many employees and guests in attendance produce a minimum cost? What is the minimum cost for this event?
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You have quadratic function with a=1/2, b = -10 and c=80
The lowest point, or minimum, occurs when n = -b/2a = 10/(2*(1/2)) = 10
The minimum cost is P(10) = (1/2)10^2-10*10+80 = 50-100+80 = $30
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3. In the formula N = Ie^(kt),
N is the number of items in terms of an initial population I at a given time t and
k is a growth constant equal to the percent of growth per unit time.
There are currently 45 million cars in a certain country, increasing by 3.2% annually.
How many years will it take for this country to have 61 million cars. Round to the nearest year.
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61 million = (45 million)e^(0.032t)
1.356 = e^(0.032t)
Take the natural log of both sides to get:
0.032t = ln(1.356)
t = 9.5168.. years
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Cheers,
Stan H.
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