Question

sung-hi is filling a sandbox with sand at the rate shown in the table below. which statement must be true regarding the linear function that represents this situation?

\

$$\begin{tabular}{|l|c|c|c|c|c|} \\hline \\multicolumn{6}{|c|}{amount of sand in the sandbox} \\\\ \\hline number of minutes since sung-hi started & 0 & 1 & 2 & 3 & 4 \\\\ \\hline amount of sand in the sandbox (pounds) & 200 & 220 & 240 & 260 & 280 \\\\ \\hline \\end{tabular}$$

• the initial value must be 0 pounds.
• the initial value must be 20 pounds.
• the rate of change must be 0 pounds per minute.
• the rate of change must be 20 pounds per minute.

Explanation:

Determine the initial value

$$ \text{Initial Value} = y(0) = 200\text{ pounds} $$

Calculate the rate of change

$$ \text{Rate of Change} = \frac{220 - 200}{1 - 0} = 20\text{ pounds per minute} $$

Evaluate the given statements

$$
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$$

Answer:

• The initial value must be 0 pounds.
• The initial value must be 20 pounds.
• The rate of change must be 0 pounds per minute.
• The rate of change must be 20 pounds per minute. (Correct answer)