Question

let n be the number of oil refineries at t years since 2003. a reasonable model of the number of oil refineries is n = -3.24t + 147.62.
a. what is the slope? what does it mean in this situation?
b. what is the n-intercept? what does it mean in this situation?
c. predict the number of refineries in 2013.

a. it means that the number of refineries are decreasing by about 147.62 per year.
b. it means that the number of refineries are decreasing by about 3.24 per year.
c. it means the number of refineries in 2003 was about 3.24.
d. it means the number of refineries in 2003 was about 147.62.
b. what is the n-intercept?
(type an ordered pair.)

Explanation:

Step1: Recall the slope-intercept form

The slope - intercept form of a linear equation is \(n = mt + b\), where \(m\) is the slope and \(b\) is the \(n\) - intercept (when \(t = 0\)). For the equation \(n=-3.24t + 147.62\), the slope \(m=-3.24\) and the \(n\) - intercept occurs when \(t = 0\).

Step2: Find the n - intercept

To find the \(n\) - intercept, we set \(t = 0\) (since \(t\) represents the number of years since 2003, \(t = 0\) corresponds to the year 2003).
Substitute \(t = 0\) into the equation \(n=-3.24t+147.62\):
\(n=-3.24\times0 + 147.62=147.62\)
So the ordered pair for the \(n\) - intercept is \((0,147.62)\) because when \(t = 0\) (the year 2003), \(n = 147.62\).

Answer:

\((0,147.62)\)