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Tom bought a boat for $\$3,000$ and incurs a daily storage fee of $\$15$ . Write a linear function to represent the total amount Tom will owe, $p(x)$ , if he waits $x$ days to pick it up. $\newline$ ______

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Write linear functions: word problems

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Q. Tom bought a boat for

\$3,000

and incurs a daily storage fee of

\$15

. Write a linear function to represent the total amount Tom will owe,

p(x)

, if he waits

x

days to pick it up.

\newline

______

Identify Cost and Fee: Identify the initial cost and the daily storage fee. $\newline$ Tom bought the boat for an initial cost of $\$3,000$ . This is a one-time payment and does not depend on the number of days. The daily storage fee is $\$15$ per day. This fee accumulates each day Tom waits to pick up the boat.
Write Linear Function: Write the linear function to represent the total cost. $\newline$ The total amount Tom will owe, $p(x)$ , is the sum of the initial cost and the daily storage fees accumulated over $x$ days. The linear function will have a constant term (the initial cost) and a variable term (the daily fee times the number of days). $\newline$ $p(x) = \text{initial cost} + (\text{daily storage fee} \times \text{number of days})$ $\newline$ $p(x) = (\$3,000) + (\$(15) \times x)$
Simplify Function: Simplify the linear function. $\newline$ The linear function does not need any further simplification since it is already in the form of $p(x) = mx + b$ , where $m$ is the slope (daily storage fee) and $b$ is the y-intercept (initial cost). $\newline$ $p(x) = \$(3,000) + \$(15)x$

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