Some scientists believe that the average surface temperature of the world has been rising steadily. They have modeled the temperature by the linear function T = 0.02t + 8.75, where T is temperature in °C and t represents years since 1900.

(a) What do the slope and T-intercept represent?

The slope is _______ , which means that the average surface temperature of the planet is increasing or decreasing at a rate of ______°C per year. The T-intercept is _______ , which presents the average surface temperature in the year _______ .

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

(a) The slope of the linear function, 0.02, represents the rate of change of the average surface temperature of the planet. In this case, the slope indicates that the average surface temperature is increasing at a rate of 0.02°C per year.

The T-intercept of the linear function, 8.75, represents the value of T when t is 0. In other words, it represents the average surface temperature in the year 1900.

(b) To predict the average global surface temperature in 2100, we need to substitute t = 2100 - 1900 = 200 into the linear function:

T = 0.02t + 8.75
T = 0.02(200) + 8.75
T = 4 + 8.75
T = 12.75°C

Therefore, the predicted average global surface temperature in 2100 is 12.75°C.

(a) In the given linear function T = 0.02t + 8.75:

- The slope, 0.02, represents the rate at which the average surface temperature of the planet is changing over time. It indicates that for every year passed since 1900, the temperature increases by 0.02°C.
- The T-intercept, 8.75, represents the average surface temperature in the year 1900.

(b) To predict the average global surface temperature in 2100 using the equation T = 0.02t + 8.75, we first need to determine the value of t for the year 2100. Since t represents years since 1900, the year 2100 would be 2100 - 1900 = 200.

Now, substitute t = 200 into the equation:
T = 0.02(200) + 8.75
T = 4 + 8.75
T = 12.75°C

Therefore, the predicted average global surface temperature in 2100 is 12.75°C.

think back to your Algebra I and these answers should be clear. Any ideas?