Final answer:
The linear function representing the number of pages typed as a function of time is p = (1/10)t - 1, with t (time in minutes) being greater than or equal to 0. The slope is 1/10 pages per minute, representing how many pages can be typed per minute on average.
Step-by-step explanation:
To find a linear function that represents the number of pages typed, p, as a function of time, t, we need to establish two points that we can use to determine the slope of the linear function. We are given that four pages can be typed in 50 minutes and nine pages in 100 minutes (since one hour and forty minutes is the same as 100 minutes). To find the slope, which is the rate at which pages are typed, we can use the formula (slope) = (change in p) / (change in t). With our points (50, 4) and (100, 9), the slope is (9 - 4) / (100 - 50) = 5 / 50 = 1/10 pages per minute.
Next, we use one of the points to find the y-intercept (the starting point at t=0). The linear equation takes the form p = mt + b where m is the slope and b is the y-intercept. To find b, we can use one of our points, say (50, 4):
4 = (1/10) * 50 + b
b = 4 - 5 = -1
Thus, the linear function is:
p = (1/10)t - 1
Regarding the values of t that make sense for this example, since the time can't be negative when typing, t should be greater than or equal to 0. Also, t should be realistically within the working hours of the typist.