MAT100-30 COLLEGE ALGEBRA 2023-2 $\leftarrow 11.01$ - Linear Function Ap... CURRENT OBJECTIVE Represent a real-world application as a linear function 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. If $C(t)$ is the number of credits after $t$ semesters, which of these equations correctly represents this situation? Select the correct answer below: $C(t)=13 t+8$ $C(t)=10 t+18$ $C(t)=12 t+6$ $C(t)=12 t+10$ $C(t)=10 t+14$

Step 1 ：The problem is asking for a linear function that represents the number of credits a student has after t semesters. We know that the student had 34 credits after 2 semesters and 58 credits after 4 semesters. We can use these two points to find the slope of the line, which represents the number of credits the student earns each semester. The y-intercept of the line represents the number of credits the student had before starting college.

Step 2 ：Calculate the slope using the formula: \(slope = \frac{y_2 - y_1}{x_2 - x_1}\). Substituting the given points (2, 34) and (4, 58), we get \(slope = \frac{58 - 34}{4 - 2} = 12\).

Step 3 ：Calculate the y-intercept using the formula: \(y = mx + c\). Substituting the given point (2, 34) and the calculated slope 12, we get \(34 = 12*2 + c\), which simplifies to \(c = 10\).

Step 4 ：The slope of the line, which represents the number of credits the student earns each semester, is 12. The y-intercept of the line, which represents the number of credits the student had before starting college, is 10. Therefore, the equation that represents this situation is \(C(t)=12 t+10\).

Step 5 ：Final Answer: \(\boxed{C(t)=12 t+10}\)