A technology specialist studied the relationship between time spent on social media and age. One observation found that a 50-year-old person spends 6 hour per week on social media. A second observation showed that a 20-year-old person spends 18 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.

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 6 hour per week on social media. A second observation showed that a 20-year-old person spends 18 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.

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Answer 1

Bot GPT 3.5 answered
2 months ago

To find a linear model relating time spent on social media to age, we can use the two observations given to determine the equation of the line.

Let (a1, T1) = (50, 6) be the first observation and (a2, T2) = (20, 18) be the second observation.

We can use the formula for the equation of a line given two points:

T - T1 = ((T2 - T1)/(a2 - a1)) * (a - a1)

Substitute in the given values:

T - 6 = ((18 - 6)/(20 - 50)) * (a - 50)

T - 6 = (12/-30) * (a - 50)

T - 6 = -0.4a + 20

T = -0.4a + 26

Therefore, the linear model relating time spent on social media to age is:

T = -0.4a + 26.