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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 $ ^{\circ} 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 yearly increase in surface temperature of the earth

T-intercept represents the surface temperature of the earth in the year $1900 .$

b. $T=12.5^{\circ} C$

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all right, so we have a situation being modelled by this equation. Lower case T stands for the number of years since the year 1900 Capital T stands for the temperature of the surface of the earth, the average temperature in degrees Celsius. And so let's talk about the slope slope is always rate of change, and when you want to figure out the slope, it helps. If you analyze the units of your rate of change, remember, it's changing. Why over change in X in this case are wise capital T temperature and our X is lower case t time. So it's changing temperature over change in time, and that would be the change in temperature in degrees Celsius per year. So it's telling us how much the temperature is going up every year. It's telling us the rise in temperature per year about the Y intercept. Well, in this case, the Y intercept is 8.5, and what does that mean? That would be the temperature when the time is zero. When the time is zero means when it is the year 1900. So that tells us the Earth's surface average temperature in the year 1900. Okay for the next part. What we want to do is use this model to predict the average global surface of the earth temperature in the year 2000 20. 100 2100. So that year is 200 years since the year 1900. So it's t equals 200. So we're going to substitute that into our equation. So we have capital t equals 0.2 times 200 for the time, plus 8.5. And when we multiply it 0.2 by 200 we get four. And when we have these together we get 12.5. So what that's telling us is that we're expecting, according to this model, that the Earth's surface will be 12.5 degrees. Oops, Sorry about that. Try that again. 12.5 degrees Celsius in the year. 2100