Final answer:
To determine how long it will take for the printer to use all 69 sheets, we solve the equation p(t) = -6t + 69 by setting it to zero and find that t equals 11.5 minutes.
Step-by-step explanation:
To find out when the printer will use all 69 sheets of paper, we set the equation p(t) = −6t + 69 equal to zero, since p(t) represents the number of sheets left after t minutes. Setting the equation to zero gives us 0 = −6t + 69. To solve for t, we need to isolate t on one side of the equation. Doing so, we get:
6t = 69
Then, divide both sides by 6:
t = 69 / 6
t = 11.5
Thus, it will take 11.5 minutes for the printer to use all 69 sheets of paper.
To find the number of minutes it would take the printer to use all 69 sheets of paper, we need to find the value of t when p(t) = 0.
Given the function p(t) = -6t + 69, we substitute 0 for p(t) and solve for t:
0 = -6t + 69
6t = 69
t = 69/6
t = 11.5
Therefore, it would take the printer approximately 11.5 minutes to use all 69 sheets of paper.