Question

Terry is skiing down a steep hill. Terry's elevation, E, in feet after t seconds is given by E = 3500 - 80 t , Where t can be any number from 0 to 10.Interpret the following using the language and situation in the problem (don't just give a definition of the algebraic object):(a) What is the meaning of -80t in the equation, with regards to Terry skiing down a steep hill?(b) What is the meaning of the number 3500 in the equation, with regards to Terry skiing down a steep hill?

Answer 1

Given the function below

$E=3500-80t$

a) This is the equation of the line into slope intercept form

The slope(m) is equal to

$m=-80\frac{ft}{sec}$

The slope is negative, because is decreasing.

Therefore, the elevation is decreasing by 80 feet each second.

b) The E-intercept is the value of E when the value of t is equal to zero

Substitute t = 0 into the equation

$\begin{gathered} E=3500-80(0)=3500-0=3500 \\ \therefore E=3500 \end{gathered}$

Therefore, the equation tells us that Terry started at an elevation of 3,500ft.