Question

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.

Answer 1

The slope of the linear function represents the rate of temperature increase per year while the T-intercept represents the estimated global surface temperature in 1900. Substituting t=200 into the equation predicts an average global surface temperature of 12.50°C in 2100.

Step-by-step explanation:

Understanding the Linear Model of Earth's Temperature Rise

The linear function given is T = 0.02t + 8.50, where T is the temperature in degrees Celsius and t represents the years since 1900. The slope of this function is 0.02, which indicates the average rate at which the average global surface temperature is increasing per year. The T-intercept is 8.50°C, which can be interpreted as the estimated global surface temperature in the base year, 1900.

To project the average global surface temperature in 2100, we simply substitute t = 200 into the equation (since 2100 is 200 years after 1900) and calculate:

T = 0.02(200) + 8.50 = 4 + 8.50 = 12.50°C

Therefore, using this model, the predicted average global surface temperature in 2100 is 12.50°C.

Answer 2

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