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.

b. predict the enrollment when it has been 7 years since the college opened.
18 thousand students
(type a whole number.)
c. predict when the enrollment will reach 24 thousand students.
□ years
(type a whole number.)

Explanation:

Step1: Find the linear equation

First, we determine the slope \( m \) of the line using two points. Let's take \( (t_1, E_1) = (0, 4) \) and \( (t_2, E_2) = (1, 6) \). The slope formula is \( m=\frac{E_2 - E_1}{t_2 - t_1} \). So \( m=\frac{6 - 4}{1 - 0}=2 \). The y - intercept \( b \) is the value of \( E \) when \( t = 0 \), so \( b = 4 \). The linear equation is \( E=2t + 4 \).

Step2: Solve for t when E = 24

We substitute \( E = 24 \) into the equation \( E=2t + 4 \). So we have the equation \( 24=2t + 4 \). Subtract 4 from both sides: \( 24-4=2t \), which simplifies to \( 20 = 2t \). Then divide both sides by 2: \( t=\frac{20}{2}=10 \).

Answer:

10