Question

The summit of Africa's largest peak, Mt. Kilimanjaro, consists of the northern and southern ice fields and the Furtwangler glacier. In 2000 the Furtwangler glacier covered an area of 60,000 m2. By 2012, the area of the glacier has shrunk 1 to approximately 25,000 m2. (a) If this decline is modeled by a linear function, find A=f(t), the equation of ice cover area as a function of time.

Answer 1

Answer:

The equation of ice cover area as a function of time is $A(t)=-\frac{8750}{3}+60000$

Step-by-step explanation:

If y = f(x) is a linear function, then for some constants b and m:

                                                $y=b+mx$

where,

• m is called the slope, and gives the rate of change of y with respect to x. Thus,

                                                     $m=\frac{\Delta y}{\Delta x} =\frac{y_2-y_1}{x_2-x_1}$

• b is called the vertical intercept, or y-intercept, and gives the value of y for x = 0.  In mathematical models, b typically represents an initial, or starting, value of the output.

To find the equation of ice cover area as a function of time, $A=f(t)$.

We know that,

In 2000 (t = 0) the Furtwangler glacier covered an area of 60,000 $m^2$ ($A_1$).

In 2012 (t = 12) the area of the glacier has shrunk to approximately 25,000 $m^2$ ($A_2$).

So,

The slope is:

$m=\frac{A_2-A_1}{t_2-t_1}= \frac{25000-60000}{12-0} =-\frac{35000}{12}=-\frac{8750}{3}\:\frac{m^2}{year}$

and the y-intercept is 60,000 $m^2$.

Therefore, the linear function is:

$A(t)=-\frac{8750}{3}+60000$