Activity 1.4.3.
The summit of Africa’s largest peak, Mt. Kilimanjaro, has two main ice fields and a glacier at its peak. Geologists measured the ice cover in the year 2000 (\(t = 0\)) to be approximately \(1951\) m\(^2\text{;}\) in the year 2007, the ice cover measured \(1555\) m\(^2\text{.}\)
(a)
Suppose that the amount of ice cover at the peak of Mt. Kilimanjaro is changing at a constant average rate from year to year. Find a linear model \(A = f(t)\) whose output is the area of the ice cover, \(A\text{,}\) in square meters in year \(t\) (where \(t\) is the number of years after 2000).
(b)
What do the slope and \(A\)-intercept mean in the model you found in (a)? In particular, what are the units on the slope?
(c)
Compute \(f(17)\text{.}\) What does this quantity measure? Write a complete sentence to explain.
(d)
If the model holds further into the future, when do we predict the ice cover will vanish?
(e)
In light of your work above, what is a reasonable domain to use for the model \(A = f(t)\text{?}\) What is the corresponding range?
The main context of the sequence of questions in this activity comes from Exercise 30 on p. 27 of Connally’s Functions Modeling Change, 5th ed.
