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Accounting functions are embedded and determined

Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for the number of cups you sell as a 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
-1
0
1
2

f(x)
-1
1
3
5
7

3. Which of the following are functions? Explain your reasoning for a, b, and c. Keep the definition of a function strongly in mind as you do this problem, it is not nearly as difficult as it may look. Think about whether the relationship between f(x) and x is consistent with being a function or not and explain your reasoning. Problems b & c are multi part relations so consider all parts when deteriming if they are funcitons.

a. f(x) = x + 4

b. f(x) = 3 if x>2 otherwise f(x) = -2

c. f(x) = 7 if x>0 or f(x) = -7 if x<0 or f(x) = 7 or -7 if x = 0

4. For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function. Explain your reasoning thoroughly.

a. The time it takes you to get to work as a function the speed at which you drive

b. The probability of getting into a car accident as a function of the speed at which you drive

c. A person's height as a function of the person's age (from age 0 to 100)

Solution Preview

See the attached file for graph and clearer layout.

Suppose you have a lemonade stand, and when you charge $2 per cup of lemonade you sell 120 cups. But when you raise your price to $3 you only sell 60 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for number of cups, and "P" for the price you charge. Assume the function is linear.
You have two points: (2,120), (3,60) so you need to find the slope: [120-60]/[2-3] = -60
Find the intercept using c=60 when p=3 and m=-60:
60 = -60*3+b
60 = -180 + b
b = 240
THE EQUATION is c = -60p + 240

2. Take a look at the table below and write out an equation for f(x) I guessed that this was what it actually looked like...
x -2 -1 0 1 2
f(x) -1 1 3 5 7

First we plot the points in Excel or a graph paper:

The graph is a straight line of the type: y = f(x) = mx + b
Now, take any two points from the table, plug them into the equation and solve for m and b.
For x = 0, f(x) = 3, 3 = m*0+b which gives b = 3.
This equation is y = f(x) = mx + 3
For x = 1, ...

Solution Summary

Accounting functions are determined. A linear function is analyzed.

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