Word Problem

Question

Grinnell Glacier National Park in the US covered about 142 acres in 2007 and was shrinking at a rate of about 4.4% per year.

 

(a) Write a formula for the size, S, of the Grinnell Glacier, in acres, as a function of years t since 2007.

 

(b) Use the model to predict the size of the glacier in the year 2015.

Answer 1

I have always found these types of questions are easiest to conceptualize and tackle when you start evaluating the expression. Aka, you start doing the yearly calculations by hand and the "trend" (formula) will usually jump out at you. 

 

So, here is what we know. 

 

Year 2007: S(2007) = 142

Year 2008: S(2008) = 142 * (1 - 0.044) = 142 * .956 = 135.75

Year 2009: S(2009) = 135.75 * (1 - 0.044) = 135.75 * .956 = 129.78

Etc

Etc

 

Do you see the "trend"? 

 

Year 2007: S(2007) = 142

Year 2008: S(2008) = S(2007) * .956

Year 2009: S(2009) = S(2008) * .956 = S(2007) * .956² 

Etc

Year(X): S(X) = S(2007) * .956^(x-2007) = 142 * .956^(x-2007)