Question

A college student takes the same number of credits each semester. Before beginning college, the student had some credits

earned while in high school. After 2 semesters, the student had 34 credits, and after 4 semesters, the student had 58
credits.

Answer 1

Final answer:

The student's mathematics problem involves solving for the number of credits they started with and the number taken each semester. By creating linear equations and solving for the unknowns, we find the student had 10 credits prior to college and takes 12 credits each semester.

Step-by-step explanation:

The question presented is a mathematics problem that involves a linear relationship. The student earned some credits in high school and is taking a consistent number of credits each semester in college. After two semesters, the student had a total of 34 credits, and after four semesters, the student had 58 credits. To determine how many credits the student started with before college and how many credits the student takes each semester, we can set up two linear equations based on the information given and solve for the two unknowns.

Let's let x be the number of credits the student started with and y be the number of credits the student takes each semester. After 2 semesters, the equation would be:

2y + x = 34 (1)

After 4 semesters, the equation would be:

4y + x = 58 (2)

By subtracting equation (1) from equation (2), we eliminate x and get:

2y = 24

Dividing both sides by 2, we find that y = 12. This means the student enrolls in 12 credits each semester. Plugging y back into equation (1), we can solve for x:

2(12) + x = 34

24 + x = 34

x = 10. So the student had 10 credits before beginning college.

Answer 2

C(t) = 12t + 10

Step-by-step explanation:

We're given two data points, (2,34) and (4,58). We want to find an equation of the form C(t)=mt+b where m is the rate of change and b is the y-intercept.

First, we find the rate of change.

m=(58−34)/(4−2)

m=24/2

m=12

This rate of change means that the student earns 12 credits each semester.

Finally, we need to solve the equation C(t)=12t+b for b, or the y-intercept. We do this by plugging in one of our data points. We'll use (2,34).

C(t)=12t+b

34=12(2)+b

b=34−24

b=10

This y-intercept means that the student earned 10 credits in high school.

Now that we've found m and b based on the given data, we find that the equation is C(t)=12t+10.