Question

Some scientists believe that the average surface temperature of the world has been rising steadily. The average surface temperature can be modeled by T = 0.02t + 15.0. where T is temperature in ∘C and t is years since 1950.

(a) What do the slope and T-intercept represent?
(b) Use the equation to predict the average global surface temperature in 2050.

Answer 1

(a)

The slope of the equation = 0.02

Therefore T-intercept equals 15

(b)

Therefore the average global surface temperature in 2050 is 17°C.

Explanation:

If a equation is in the form

y= mx+c........(1)

Then the slope of the equation is m.

Slope: The tangent of the angle which is made with the positive x-axis.

If θ be the angle , Then slope (m)= tanθ.

If a equation in the form

`(x)/(a) +(y)/(b) =1`............(2)

Then x-axis intercept equals a and y-axis intercept equals b.

Given equation is

T=0.02t+15.0

Comparing with equation (1)

The slope of the equation = 0.02

Again we can rewrite the equation as

`T-0.02t=15`

`\Rightarrow (T)/(15) -(0.02t)/(15)=1`

Comparing with (2)

Therefore T-intercept equals 15

(b)

Here t= 2050-1950 =100

Putting t=100 in the given equation

T=0.02(100)+15 = 2+15 =17

Therefore the average global surface temperature in 2050 is 17°C.