Question

Some scientists believe that the average surface temperature of the world has been rising steadily. They have modeled the temperature by the linear function\({\bf{T = 0}}{\bf{.02t + 8}}{\bf{.5}}\), where\({\bf{T}}\)is the temperature in\({}^{\bf{o}}{\bf{C}}\)and\({\bf{t}}\)represents years since 1900.

(a) What do the slope and\({\bf{T}}\)-intercept represent?

(b) Use the equation to predict the average global surface temperature in 2100.

Short answer

1. The slope\(m = 0.02\)represents thechange in the average global temperature per year. And\(T\)-intercept represents the average global surface temperature at\(t = 0\)
2. The temperature in the 2100 year is\({12.50^ \circ }C\).

Step-by-step solution

Given data

The relation between\(T\)and \(t\)is given by:

\(T = 0.02t + 8.50\)

(a) Determine the slope and \({\bf{T}}\)-intercept represent

Slope\(m = 0.02\)

\(\)

\(T\)-intercept =\(8.50\)

Here,\(m = 0.02\)represents the change in the average global temperature per year.

And \(T\)-intercept represents the average global surface temperature at \(t = 0\).

(b) Determine the average global surface temperature in 2100

When at the year 2100 then,

\(\begin{array}{l}t = 2100 - 1900\\\;\; = 200\end{array}\)

Temperature,

\(\begin{array}{l}T = 0.02 \times 200 + 8.50\\\;\;\; = 4 + 8.50\\\;\;\; = {12.50^ \circ }C\end{array}\)

Hence, the temperature in the 2100 year is\({12.50^ \circ }C\).