Chapter 3, Problem 106RE

Global temperatures have been rising, on average, for more than a century, sparking concern that the polar ice will melt and sea levels will rise. With t in years since 1880, fitting functions to the data1 gives three models for the average global temperature in Celsius:

f(t) = 13.625 + 0.006t

g(t) = 0.00006t² − 0.0017t + 13.788

ℎ(t) = 13.63e^0.0004t .

1. (a) What family of functions is used in each model?
2. (b) Find the rate of change of temperature in 2010 in each of the three models. Give units.
3. (c) For each model, find the change in temperature over a 130-year period if the temperature had been changing at the rate you found in part (b) for that model.
4. (d) For each model, find the predicted change in temperature for the 130 years from 1880 to 2010.
5. (e) For which model, if any, are the answers equal in parts (c) and (d)?
6. (f) For which model is the discrepancy largest between the answers in parts (c) and (d)?