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QUESTION

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 &amp. 5, we can get easily get the value of a &amp. 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.

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