Precal Homework...

Question

The summit of Africa's largest peak, Mt. Kilimanjaro, consists of the northern and southern ice fields and the Furtwanger glacier. An article in the Proceedings of the National Academy of Sciences indicates that in 2000 (t=0) the area of the ice cover at the peak of Mt. Kilimanjaro was approximately 1951 m². By 2007, the area had shrunk to approximately 1555m². 

 

a.) If this decline is modeled by a linear function, find A=f(t), the equation of the ice-cover area as a function of time.

 

b.) Evaluate f(11)

 

c.) If this model is correct, when would you expect the ice cover to disappear?

Answer 1

When t = 0, A = 1951  So, (0, 1951) is a point on the line

When t = 7, A = 1555  So, (7, 1555) is a point on the line

 

Slope = (1555-1951)/(7-0) ≈ -56.57

 

Using the point-slope form, A - 1951 = -56.57(t - 0)

 

So, A = f(t) = -56.57t + 1951

 

f(11) = -56.57(11) + 1951 ≈ 1329 m²

 

The ice cover will disappear when f(t) = 0

 

   -56.57t + 1951 = 0

 

             -56.57t = -1951

 

                     t = 34.5 years

 

The ice cover will vanish in about 34.5 years from the time that the ice-cover was first measured in the year 2000.