Question

let e be a colleges enrollment (in thousands of students) at t years since the college began. some pairs of values of t and e are shown in the table.
t (years) | e (thousands of students)
0 | 4
1 | 6
2 | 8
3 | 10
4 | 12

b. predict the enrollment when it has been 7 years since the college opened.
thousand students
(type a whole number.)

Explanation:

Step1: Identify the pattern

From the table, when \( t = 0 \), \( E = 4 \); \( t = 1 \), \( E = 6 \); \( t = 2 \), \( E = 8 \); \( t = 3 \), \( E = 10 \); \( t = 4 \), \( E = 12 \). The difference in \( E \) for each increase in \( t \) by 1 is \( 6 - 4 = 2 \), \( 8 - 6 = 2 \), etc. So the relationship is linear with slope \( m = 2 \) and y - intercept \( b = 4 \). The equation is \( E = 2t + 4 \).

Step2: Substitute \( t = 7 \)

Substitute \( t = 7 \) into the equation \( E = 2t + 4 \). So \( E = 2(7)+4 = 14 + 4 = 18 \).

Answer:

18