Question

Constant check is being carried out by researchers on the area of a glacier in Canada. The glacier is slowly shrinking. The glacier orginally occupied 15000 miles, but after two years of monitoring the glacier, the scientists document that the area of the glacier is now 14910 square miles. If x is the number of years since monitoring began, which equation best describes the glacier's area, G(x), as a function of time?

• A. $G\left(y\right)=15000\frac{1}{x}$
• B. $G\left(y\right)=15000{\left(0.003\right)}^x$
• C. $G\left(y\right)=15000{\left(0.997\right)}^x$
• D. $G\left(y\right)={0.997}^x$

Answer 1

The correct option is C $G\left(y\right)=15000{\left(0.997\right)}^x$

Decrease in the area of the glacier since monitoring is $15000-14910=90$ sq. miles

Decrease (%) $=\frac{90}{15000}\times 100$

Decrease (%) $=0.6$ i.e. $99.4\%$

Also, $(0.997{)}^2=0.994$

Since the monitoring was being carried out for 2 years, the equation that best describes the area of the glacier is

$G\left(y\right)=15000(0.997{)}^x$

So, if we substitute $x=2$ in the above equation, we get the value of $G\left(y\right)$ as $14910$ sq. miles