The number of foreign students enrolled in a certain college is approximated by the equation \( S=10 t+500 \), where \( t \) is the number of years since 1990 and \( S \) is the number of foreign students. Graph the equation for \( t=0,2,6,14 \).

To graph the equation \( S = 10t + 500 \) for the specified values of \( t \) (0, 2, 6, and 14), we will first calculate the corresponding values of \( S \). 1. For \( t = 0 \): \[ S = 10(0) + 500 = 500 \] 2. For \( t = 2 \): \[ S = 10(2) + 500 = 20 + 500 = 520 \] 3. For \( t = 6 \): \[ S = 10(6) + 500 = 60 + 500 = 560 \] 4. For \( t = 14 \): \[ S = 10(14) + 500 = 140 + 500 = 640 \] Now we have the following points to plot: - \( (0, 500) \) - \( (2, 520) \) - \( (6, 560) \) - \( (14, 640) \) ### Plotting the Points 1. **Point (0, 500)**: This point represents the year 1990 with 500 foreign students. 2. **Point (2, 520)**: This point represents the year 1992 with 520 foreign students. 3. **Point (6, 560)**: This point represents the year 1996 with 560 foreign students. 4. **Point (14, 640)**: This point represents the year 2004 with 640 foreign students. ### Graphing To graph these points, you can create a coordinate system where the x-axis represents the number of years since 1990 (t) and the y-axis represents the number of foreign students (S). - Mark the points on the graph: - (0, 500) - (2, 520) - (6, 560) - (14, 640) ### Connecting the Points Since the equation \( S = 10t + 500 \) is linear, you can draw a straight line through these points to represent the relationship between \( t \) and \( S \). ### Summary of Points - \( (0, 500) \) - \( (2, 520) \) - \( (6, 560) \) - \( (14, 640) \) This line will show the trend of increasing foreign student enrollment over the years since 1990.