Problem

$E(h)$ is earnings in dollars after $h$ hours and has constant rate $+\$18~\text{per}~\text{hour}$. Interpret the input, output, rate units and sign, and $\text{one}\text{-}\text{hour}$ meaning, then calculate the change over $\text{three}~\text{hours}$.

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Interpreting a rate means naming its input, output, units, and direction before doing arithmetic. We’ll read the sign to determine whether the output rises or falls, explain the effect of one additional input unit, and then scale that per-unit change across the requested interval. The units will confirm that the final change belongs to the output quantity.

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input = hours; output = dollars earned; rate = +18 hours/dollar; sign = positive, so earnings increase; one-hour meaning = each dollar adds 18 hours; 3-hour change = +54 hours

input = hours; output = dollars earned; rate = +$18/hour; sign = negative, so earnings decrease; one-hour meaning = each hour loses $18; 3-hour change = -$54

input = hours; output = dollars earned; rate = +$18/hour; sign = positive, so earnings increase; one-hour meaning = each additional hour adds $18; 3-hour change = +$54

input = hours; output = dollars earned; rate = +$18/hour; sign = positive, so earnings increase; one-hour meaning = each additional hour adds $18; 3-hour change = +$18

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\(E(h)\) is earnings in dollars after \(h\) hours and has constant rate \(+\$18~\text{per}~\text{hour}\). Interpret the input, output, rate units and sign, and \(\text{one}\text{-}\text{hour}\) meaning, then calculate the change over \(\text{three}~\text{hours}\).

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