Question

1. a car rental company charges a flat fee of $25 plus $0.20 per mile driven. which linear function models the total cost c (in dollars) for m miles, and what do the rate of change and initial value represent in the situation?

a. \\(c(m) = 0.20m + 25\\); rate of change = 25 (dollars per mile), initial value = $0.20
b. \\(c(m) = 25m + 0.20\\); rate of change = 25 (dollars per mile), initial value = $0.20
c. \\(c(m) = 0.20m + 25\\); rate of change = 0.20 (dollars per mile), initial value = $25
d. \\(c(m) = 25 + 0.20\\); rate of change = 0.20 (dollars per mile), initial value = $25

Explanation:

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<reasoning>

Identify the given values

The flat fee is \$25.
The cost per mile is \$0.20.

Formulate the linear function

The total cost \(C(m)\) depends on miles \(m\).
\[C(m) = 0.20m + 25\]

Determine the rate of change

The rate of change is the coefficient of \(m\).
It is 0.20 dollars per mile.

Determine the initial value

The initial value is the constant term.
It is \$25.

Match with the options

Option C matches all determined values.
</reasoning>

<answer>
<mcq-option>(A) \(C(m) = 0.20m + 25\); rate of change = 25 (dollars per mile), initial value = \$0.20</mcq-option>
<mcq-option>(B) \(C(m) = 25m + 0.20\); rate of change = 25 (dollars per mile), initial value = \$0.20</mcq-option>
<mcq-correct>(C) \(C(m) = 0.20m + 25\); rate of change = 0.20 (dollars per mile), initial value = \$25</mcq-correct>
<mcq-option>(D) \(C(m) = 25 + 0.20\); rate of change = 0.20 (dollars per mile), initial value = \$25</mcq-option>
</answer>

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Answer:

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<reasoning>

Identify the given values

The flat fee is \$25.
The cost per mile is \$0.20.

Formulate the linear function

The total cost \(C(m)\) depends on miles \(m\).
\[C(m) = 0.20m + 25\]

Determine the rate of change

The rate of change is the coefficient of \(m\).
It is 0.20 dollars per mile.

Determine the initial value

The initial value is the constant term.
It is \$25.

Match with the options

Option C matches all determined values.
</reasoning>

<answer>
<mcq-option>(A) \(C(m) = 0.20m + 25\); rate of change = 25 (dollars per mile), initial value = \$0.20</mcq-option>
<mcq-option>(B) \(C(m) = 25m + 0.20\); rate of change = 25 (dollars per mile), initial value = \$0.20</mcq-option>
<mcq-correct>(C) \(C(m) = 0.20m + 25\); rate of change = 0.20 (dollars per mile), initial value = \$25</mcq-correct>
<mcq-option>(D) \(C(m) = 25 + 0.20\); rate of change = 0.20 (dollars per mile), initial value = \$25</mcq-option>
</answer>

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