The problem describes the relationship between the amount of time a car is parked and the cost of parking. We need to identify the independent and dependent variables, describe the function in a sentence, sketch a graph of the function given a cost of $3 per hour with a maximum cost of $12, and identify one point on the graph and explain its meaning.

1. Problem Description

The problem describes the relationship between the amount of time a car is parked and the cost of parking. We need to identify the independent and dependent variables, describe the function in a sentence, sketch a graph of the function given a cost of $3 per hour with a maximum cost of$12, and identify one point on the graph and explain its meaning.

2. Solution Steps

a. Identify the independent and dependent variables.

The independent variable is the amount of time a car is parked, in hours. The dependent variable is the cost of parking, in dollars.

b. Describe the function with a sentence.

The cost of parking is a function of the amount of time parked.

c. Sketch a graph of the function.

The cost is $3 per hour, so the cost function is$C(t) = 3t$, where$C(t)$is the cost and$t$is the time in hours. However, the maximum cost is$

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2. We need to find how many hours it takes to reach the maximum cost.

$3t = 12$

$t = 12/3 = 4$

So, the cost is $3t$ for $0 \le t \le 4$, and the cost is $12 for$t > 4$.

The x-axis will be labeled "Time (hours)" and the y-axis will be labeled "Cost (dollars)". The graph will be a straight line from $(0,0)$ to $(4,12)$, and then a horizontal line at $y = 12$ for $x > 4$.

d. Identify one point on the graph and explain its meaning.

The point $(2,6)$ on the graph means that if a car is parked for 2 hours, the cost of parking is $

6. The point $(5,12)$ on the graph means that if a car is parked for 5 hours, the cost of parking is $

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2.

3. Final Answer

a. Independent variable: Amount of time parked (in hours). Dependent variable: Cost of parking (in dollars).

b. The cost of parking is a function of the amount of time parked.

c. The graph is a line from (0,0) to (4,12), then a horizontal line at y=12 for x >

4. The x-axis is labeled "Time (hours)" and the y-axis is labeled "Cost (dollars)".

d. The point (2,6) means that if a car is parked for 2 hours, the cost of parking is $

6.