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Question 1686: 1.Suppose you have a lemonade stand, and when you charge $1 per cup of lemonade you sell 60 cups. But when you raise the price to $2 you only sell 30 cups. Write an equation for the number of cups as function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear.
2. Take a look at the table below and write out an equation for f(x)
x -2-2 0 1 2
f(x) -5-2 1 4 7
3. For each of the relationships below, expalin whether you think it is best described by a linear function or non-linear function. Explain your reasoning thorougghly
a. How fast it takes you to get to work as a function of how fast you drive
b. Probility of getting into a car accident as a function of how fast you drive.
c. Your height as a fuction of age (from age 0 to 100)
Answer by khwang(438)   (Show Source):
You can put this solution on YOUR website! 1. Let C=f(P) = aP+b.
Since when P =1, C =a+b = 60...(1)
when P =2, C =2a+b = 30...(2)
(2)-(1): a = -30, so b= 60-(-30) = 90,
So, C = -30 P + 90.
2. x -2-1 0 1 2 (*you had typing error.)
f(x) -5-2 1 4 7
Assume f is linear, let f(x) = ax+b,
f(0) = b = 1,
f(1) = a + 1= 4, a =3
So,f(x) = 3x + 1
Check: f(-1) = -2+1=-2 (OK)
f(-3) = -6+1=-5 (OK)
a. How fast it takes you to get to work as a function of how fast you drive
Answer: Since the faster you drive, the shorter time it takes you to work,
So,it is not linear,in fact T = f(V) = distance/V , V: speed.
b. Probility of getting into a car accident as a function of how fast you drive.
Answer: The faster you drive, the higher probability of car accident.
So, it may be a linear function.
c. Your height as a fuction of age (from age 0 to 100)
Answer: No,since it is clear that height is not proportional to age.
Kenny
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