Question

Emma knits 2.5 cm of a sweater in an hour. The total sweater amount (s) can be represented with the equation ( s(t) = 2.5t ), where ( t ) represents the amount of hours. It took Emma 8 hours to complete her sweater. State the domain in interval notation.

a) ( t in [0, 8] )
b) ( t in (0, 8] )
c) ( t in [0, 8) )
d) ( t in (0, 8) )

Answer 1

The correct domain for the function that describes the total length of the sweater knitted over time is [0, 8], representing the time from the start to the completion of the sweater in hours.

Step-by-step explanation:

The student is tasked with finding the correct domain for the function representing the amount of sweater knitted over time, given that Emma knits 2.5 cm of a sweater in an hour. The total sweater length as a function of time can be expressed by the equation s(t) = 2.5t, where t is the number of hours spent knitting. Since it took Emma 8 hours to complete her sweater, the domain of the function is the time interval during which she was knitting. In interval notation, the domain includes the starting point at which she began, when t equals 0, up to and including the finishing point at 8 hours. Thus, the correct domain in interval notation is [0, 8].