Question

Looking back on your History class, you discovered something interesting. On your first test, you received a score of 65 points with no additional study time, other than doing your homework and attend lectures. On the second test, you decided to put in two additional hours of study time and receive a score of 85. After you have studied some mathematical modeling in math 49, you suspect that there is a relationship between your test score and the number of additional study time. Let S be your test score and T is your additional study time.

A. Assuming S and T have a linear relationship, find a formula for the linear function S=f(T).(12pts)
B. If you want a score of 98. How many hours of additional time of study would you have to put in? (3pts)

Answer 1

A. S = 65 + 10x

B. 3.3 hours

Explanation:

A. S=f(T)

65 = f(0)

85 = f(2)

S₂ - S₁

85 - 65 = 20

T₂ - T₁

2 - 0 = 2

20 / 2 = 10

For every hour you study, you will score an additional 10 points with a baseline of 65 points.

S = 65 + 10x where x is the amount of time (in hours) that you studied for.

B. S = 65 + 10x

Since we want a specific score of 98, we plug it in for S and solve for x.

98 = 65 + 10x

33 = 10x

3.3 = x

If we wanted a score of 98, we would need to study for 3.3 hours.