Jeremy uses the linear function G=12h+50 to represent the grade, G (in points out of 100), that he can earn on an exam as a function of h, the number of hours he spends studying for the exam.
1.) Identify the slope and y-intercept of Jeremy's function and explain what they mean in context of the problem.
2.) If Jeremy spends 3 hours studying for the exam, what grade does he expect to earn?
3.) How many hours should Jeremy study if he wants to earn a perfect score on the exam?
1.) The slope of Jeremy's function is 12. This means that for every additional hour he spends studying, his grade is expected to increase by 12 points. The y-intercept is 50, which means that even if Jeremy doesn't study at all (h = 0), he would still expect to earn a grade of 50 points.
2.) To calculate Jeremy's expected grade after spending 3 hours studying, we can substitute h = 3 into the function:
G = 12 * 3 + 50
G = 36 + 50
G = 86
Therefore, Jeremy expects to earn a grade of 86 points if he spends 3 hours studying for the exam.
3.) Jeremy wants to earn a perfect score on the exam, which means he needs to achieve a grade of 100 points. To find out how many hours he should study, we can set G = 100 and solve for h in the function:
100 = 12h + 50
12h = 100 - 50
12h = 50
h = 50/12
h ≈ 4.17
So, Jeremy should study for approximately 4.17 hours if he wants to earn a perfect score on the exam.
1.) In the linear function G = 12h + 50, the slope is 12, and the y-intercept is 50.
The slope represents the rate of change and indicates how much the grade (G) will increase for each additional hour (h) of studying. In this case, a slope of 12 means that for every hour Jeremy spends studying, his grade is expected to increase by 12 points.
The y-intercept represents the grade Jeremy would expect to earn if he didn't study at all. In this case, the y-intercept of 50 indicates that if Jeremy didn't study for the exam, he would still be expected to receive a grade of 50 points.
2.) If Jeremy spends 3 hours studying for the exam, we can substitute h = 3 into the equation G = 12h + 50:
G = 12(3) + 50
G = 36 + 50
G = 86
Therefore, Jeremy expects to earn a grade of 86 points if he spends 3 hours studying for the exam.
3.) To find out how many hours Jeremy should study to earn a perfect score on the exam, we substitute G = 100 into the equation G = 12h + 50 and solve for h:
100 = 12h + 50
12h = 100 - 50
12h = 50
h = 50 / 12
h ≈ 4.17
Therefore, Jeremy should study for approximately 4.17 hours (or 4 hours and 10 minutes) if he wants to earn a perfect score of 100 on the exam.
1.) To identify the slope and y-intercept of Jeremy's function, observe the function given: G = 12h + 50. In this equation, the coefficient of h, which is 12, represents the slope. The constant term, 50, is the y-intercept.
In the context of the problem, the slope, which is 12, indicates how the grade changes in relation to the number of hours spent studying. Every additional hour of studying increases the grade by 12 points. It shows that Jeremy's rate of improvement in his exam grade is 12 points per hour of studying.
The y-intercept, which is 50, represents the value that G, the grade, would be when h, the number of hours studied, is zero. In this case, it implies that if Jeremy didn't study at all (zero hours), he would start with a grade of 50 points. This can be interpreted as a starting point or base value for his grade, independent of any studying.
2.) To determine the grade Jeremy expects to earn after studying for 3 hours, substitute h = 3 into the function G = 12h + 50:
G = 12(3) + 50
G = 36 + 50
G = 86
Therefore, Jeremy expects to earn a grade of 86 points after studying for 3 hours.
3.) To find out how many hours Jeremy should study to earn a perfect score on the exam, set G (the grade) to 100 (a perfect score) in the function G = 12h + 50:
100 = 12h + 50
Next, solve for h:
100 - 50 = 12h
50 = 12h
h = 50/12
So, Jeremy would need to study approximately 4.17 hours (or 4 hours and 10 minutes) to earn a perfect score on the exam.