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You will prepare and submit a term paper on Assignment 3 High School. Your paper should be a minimum of 1500 words in length.
You will prepare and submit a term paper on Assignment 3 High School. Your paper should be a minimum of 1500 words in length. f '(x) = -2x + 200 = 0
Hence: x = 100
c. Graph the function:
Profit
The given graph is parabolic.
As expected, the profit is positive from x = 20 to x =180 verifying our answer in b. It
can also be seen that the maximum profit can be found in x = 100.
2. The population of the country is 50 million. Two months ago, the government required its citizen to purchase an identity card. After one month, 6 million people had it and by the end of the second month, 10 million people had one.
a. Model N (number of cards) as a function of t (months) using the form:
N = a + b/ (t+c)
Given are the following:
When t = 1then N = 6,000,000 hence: 6,000,000 = a + b/(1+c)[eq.1]
t = 2N = 10,000,000 hence: 10,000,000 = a + b/(2+c) [eq.2]
and of course, when
t = 0N = 0hence: 0 = a + b/c or a= -b/c [eq.3]
Simplifying eq. 1 and inserting the value of a from eq. 3, we have:
6,000,000 = -b/c + b/(1+c)
6,000,000 = (-b -bc +bc) / [c*(1+c)]
6,000,000 = -b/[c*(1+c)]but -b/c = a
6,000,000 = a / (1+c)
a = 6,000,000 + 6,000,000c [eq.4]
Simplifying eq. 1 and inserting the value of a from eq. 3, we have:
10,000,000 = -b/c + b/ (2+c)
10,000,000 = (-2b -bc +bc) / [c*(2+c)]
10,000,000 = -2b/[c*(2+c)]but -b/c = a
10,000,000 = 2a / (2+c)
a = 10,000,000 + 5,000,000c [eq.5]
By equation 4 &. 5, we can get easily get the value of a &. c:
a = 30,000,000
c =4
By eq. 3, a = - b/c or b = -ac. Hence: b = -120,000,000
The model equation is therefore:N = 30,000,000 + (-120,000,000)/ (t +4)
b.
