Question

Eric is observing the velocity of a runner at different times. After one hour, the velocity of the runner is 5 km/h. After three hours, the velocity of the runner is 3 km/h.

Part A: Write an equation in two variables in the standard form that can be used to describe the velocity of the runner at different times. Show your work and define the variables used. (5 points)

Part B: How can you graph the equations obtained in Part A for the first 5 hours? (5 points)

Answer 1

A. An infinite number of equations can be used to describe the velocity of the runner at different times. If we let v represent velocity in km/h and t represent time in hours, then we can write a linear equation as
.. v = (3 -5)/(3 -1)*(t -1)+5
.. v = -(t -1) +5
In standard form, this linear equation is
.. t +v = 6

Or, we can write an exponential equation.
.. v = 5(3/5)^((t-1)/2) . . . . . . . (value at t1)*((value at t2)/(value at t1))^((t -t1)/(t2-t1))
.. = 5√(5/3)*(√(3/5))^t
.. = 5√(5/3)*e^(ln(3/5)/2*t)
In a more or less standard form, this is
.. v = 6.4549722*e^(-0.2554128t) . . . . . . accurate to 6 decimal places


B. Graph the equation by entering it into a graphing calculator. Limit the domain as needed.