Question

A technology specialist studied the relationship between time spent on social media and age. One observation found that a 50-year-old person spends 8 hour per week on social media. A second observation showed that a 20-year-old person spends 20 hours per week on social media. Assuming time spent per week on social media T (in hr) is a linear function of age a (in yr), find a linear model of this event.

Answer 1

Use the model to find the age (in yr) of a person who spends 10 hours per week on social media.

Answer 2

To find the linear model for this relationship, we can use the two data points given to create a system of equations and then solve for the slope and y-intercept.

Let's call the time spent on social media T and the age a. Using the two observations provided:

1) When a = 50, T = 8
8 = 50m + b

2) When a = 20, T = 20
20 = 20m + b

Now we can solve this system of equations to find the values of m (slope) and b (y-intercept).

From the second equation, we get:
20 = 20m + b
b = 20 - 20m

Substitute this into the first equation:
8 = 50m + (20 - 20m)
8 = 30m + 20
30m = -12
m = -12/30
m = -0.4

Now substitute m back into the second equation to find b:
20 = 20(-0.4) + b
20 = -8 + b
b = 28

Therefore, the linear model for the relationship between time spent on social media T (in hr) and age a (in yr) is:
T = -0.4a + 28