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Sally purchased a laptop for `$800` and has to pay a service fee of `$20` for each day until it is delivered. Write a linear function to represent the total cost, $h(x)$ , after $x$ days.

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Write exponential functions: word problems

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Q. Sally purchased a laptop for `$800` and has to pay a service fee of `$20` for each day until it is delivered. Write a linear function to represent the total cost,

h(x)

, after

x

days.

Identify initial cost and rate of change: First, let's identify the initial cost and the rate of change. $\newline$ The initial cost of the laptop is $\$800$ , which is the cost Sally will pay regardless of the number of days she waits for delivery. This is the y-intercept of the linear function. $\newline$ The rate of change is the service fee of $\$20$ per day. This is the slope of the linear function.
Write linear function using slope-intercept form: Now, let's write the linear function using the slope-intercept form of a line, which is $h(x) = mx + b$ , where $m$ is the slope and $b$ is the y-intercept. $\newline$ In this case, $m$ (the slope) is $\$20$ /day, and $b$ (the y-intercept) is $\$800$ .
Substitute values into linear function: Substitute the values of $m$ and $b$ into the linear function to get the equation. $\newline$ $h(x) = 20x + 800$
Rephrase question prompt: Now, let's rephrase the question prompt to ensure that the equation answers the question asked. $\newline$ question_prompt: What is the linear function that represents the total cost, $h(x)$ , after $x$ days?

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