Question

At the beginning of the semester students reported that they spend an average of 5 hours per day watching television, decreasing at an average rate of 30 minutes per week. Professors reported that they spend an average of 1 hour per day watching television, increasing at an average rate of 30 minutes per week. (Source: Blitzer: Thinking Mathematically, 2019) a. Write a function, S, for the amount of time students watch television during week, x. b. Write a function, P, for the amount of time professors watch television during week, x. C. By which week do students and professors both watch the same number of hours of television? How many hours?

Answer 1

(a)
`X(t)=X(0)+\Delta X*t=5-0.5*t`

(b)
`X(t)=X(0)+\Delta X*t=1+0.5*t`

(c) At 4 weeks, when both will be seeing an average of 3 hours of TV.

Explanation:

a) For the students, they start at X(0)=5 h and ΔX=-0.5 h/week.

We can write

`X(t)=X(0)+\Delta X*t=5-0.5*t`

b) For the professors, they start at X(0)=1 h and ΔX=+0.5 h/week.

We can write

`X(t)=X(0)+\Delta X*t=1+0.5*t`

c) The seew which they will be watching the same amount of hours will be the 4th week.

`X(t)=5-0.5*t=1+0.5*t\\\\5-1=(0.5+0.5)*t\\\\t=4\, weeks`

The amount of hours will be

`x(4)=1+0.5*4=1+2=3\,hours`