Question

Linear Models: Glaciersm= 745-1000= -255, 15-0= 15, -255/15= -17The average annual rate of retreat of the glacier is 17 meters per year.2. Fill in the table below using the information about the average annual rate of retreatand the length of each glacier in 2010.YearLength in meters201020202030204020503. Create an equation that represents the length of the Easton Glacier as a function ofthe number of years since 2010.

Answer 1

I guess the annual retreat of the glacier is linear, and two points in the line are

`(0,1000),(15,745)`

Where x is in years and y in meters.

We can find the equation of a line given two points by using the formula below

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

In our case,

`\begin{gathered} y-1000=(745-1000)/(15-0)(x-0) \\ \Rightarrow y-1000=-17x \\ \Rightarrow y=-17x+1000 \end{gathered}`

2) Suppose that x=0 corresponds to the year 2010. Then, the information in the table is:

`\begin{gathered} 2010\to-17(0)+1000=1000 \\ 2020\to-17(10)+1000=830 \\ 2030\to-17(20)+1000=660 \\ 2040\to-17(30)+1000=490 \\ 2050\to-17(40)+1000=320 \end{gathered}`

The answers are 1000,830,660,490,320 to to bottom

c)

We already obtained the equation we are asked for in this part of the problem. Remember that we used the points (0,1000) and (15,745)

The equation is:

`y=-17x+1000`

y=-17x+1000