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. what is the slope?
m = - 3.24
what does the slope mean in this situation?

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.

Explanation:

The equation is in the form \( n = mt + b \), where \( m \) is the slope. Here, \( m=-3.24 \). The slope represents the rate of change of \( n \) with respect to \( t \) (years). A negative slope means a decrease, and the magnitude (3.24) is the amount of decrease per year. Option A refers to the y - intercept's value, C is incorrect about the slope's meaning (slope isn't the initial number), D is about the y - intercept. So the correct interpretation is in option B.

Answer:

B. It means that the number of refineries are decreasing by about 3.24 per year.