Calculus Question

Question

As a result of global warming, the area covered by the ice cap on Mt. Kilimanjaro has decreased approximately linearly, from 12.1 km2 in 1912 to 1.9 km2in 2007.

a)Let t represent the number of years since 1910. Write the area of the ice, y, as a linear function of t.

b)What does the y-intercept of this linear function represent in the context of this application?

c)Assuming that the linear function you found in part a) continues, in what year will the ice cap disappear?

Answer 1

The following is given:

t = 2007

t_o=1912

A(t) = A= 1.9 km²

A(t_o)= A_o = 12.1 km²

(a) Since the area is decreasing linearly, it can be written as:

A = A_o +r*t

where r is a negative number.

To find r, we must use the known values of the area and their respective years or

r = (A-A_o)/(t-t_o) (rise over run in a A vs t graph)

Substituting the known values we get:

r = -0.10515 km²/year

Since the problem is asking the equation since 1910 (two years prior to the given value of A_o):

A = 12.1 km² - 0.10515 km²/year*(t - 2 year)

(b) the y-intercept of this equation represents the area of the ice cap in 1910.

(c) The number of years from 1910 for which the ice cap will disappear can be obtained by making A=0 in the above equation. Inverting, we obtain, 117.07 years which is the year of 2027