Question

a computer had 2 gigabytes of data stored on it when jackie bought it, and she is storing an additional 3.5 gigabytes per year, as shown in the table below. which of these statements is correct about the linear function that represents this situation?

amount of data stored on jackies computer
\

$$\begin{array}{|c|c|c|c|c|c|} \\hline \\text{time (year)} & 0 & 1 & 2 & 3 & 4 \\\\ \\hline \\text{gigabytes of data} & 2 & 2 + 3.5 = 5.5 & 5.5 + 3.5 = 9 & 9 + 3.5 = 12.5 & 12.5 + 3.5 = 16 \\\\ \\hline \\end{array}$$

• the initial value represents the 2 gigabytes of data stored on the computer when jackie bought it, and the rate of change represents the 3.5 gigabytes per year that jackie is storing.
• the initial value represents the 2 gigabytes per year that jackie is storing, and the rate of change represents the 3.5 gigabytes of data stored on the computer when jackie bought it.
• the initial value represents the 3.5 gigabytes of data stored on the computer when jackie bought it, and the rate of change represents the 2 gigabytes per year that jackie is storing.
• the initial value represents the 3.5 gigabytes per year that jackie is storing, and the rate of change represents the 2 gigabytes of data stored on the computer when jackie bought it.

Explanation:

Identify the initial value of the linear function

$$ \text{Initial Value} = y(0) = 2\text{ gigabytes} $$

Identify the rate of change of the linear function

$$ \text{Rate of Change} = \frac{\Delta y}{\Delta x} = 3.5\text{ gigabytes per year} $$

Match with the correct statement

$$ \text{Initial Value} ightarrow 2\text{ GB (starting amount when bought)} $$

$$ \text{Rate of Change} ightarrow 3.5\text{ GB/year (additional storage per year)} $$

Answer:

• (A) The initial value represents the 2 gigabytes of data stored on the computer when Jackie bought it, and the rate of change represents the 3.5 gigabytes per year that Jackie is storing. (Correct answer)
• (B) The initial value represents the 2 gigabytes per year that Jackie is storing, and the rate of change represents the 3.5 gigabytes of data stored on the computer when Jackie bought it.
• (C) The initial value represents the 3.5 gigabytes of data stored on the computer when Jackie bought it, and the rate of change represents the 2 gigabytes per year that Jackie is storing.
• (D) The initial value represents the 3.5 gigabytes per year that Jackie is storing, and the rate of change represents the 2 gigabytes of data stored on the computer when Jackie bought it.