Recent studies indicate that the average surface temperature of the earth has been rising steadily. Some scientists have modeled the temperature by the linear function T - 0.02t 1 8.50, where T is temperature in °C and t represents years since 1900. (a) What do the slope and T-intercept represent? (b) Use the equation to predict the average global surface temperature in 2100.

a) The slope represents the change per year in the earth's surface temperature (0.02 ºC) and the T-intercept represents the average earth's surface temperature in 1900 (18.5ºC)

b) The average global surface temperature will be 22.5ºC in 2100.

Step-by-step explanation:

I think there's a "+" sign missing in the function you wrote, and that you meant to write T = 0.02t + 18.50 and I'll solve the problem for this function.

If I am wrong with the values or the + you can always substitute the values you have in your function based on the procedure I'll write down.

So, this function is T = 0.02t + 18.50.

A linear function is expressed as y = f (x) = mx + b where m is the slope of the function and b is the interception with the y-axis.

a) In this particular function, we would have that the slope of the function is 0.02 and it represents the change per year in the earth's surface temperature, since T is temperature in ºC, the change per year would be of 0.02ºC.

On the other hand, the T-intercept would be the value of the function when t=0

T (0) = 0.02 (0) + 18.50

T (0) = 18.50

This 18.50 represents the average surface temperature of the earth when measures started, meaning, the average surface temperature of the earth in 1900 was 18.50

b) To predict the average global surface temperature in 2100, we are going to substitute 200 in the function (since 2100 - 1900 = 200)

T (200) = 0.02 (200) + 18.50 = 4 + 18.50 = 22.5

Therefore, the average global surface temperature in 2100 will be 22.5ºC