Answer:
Part a) 
Part b) 
Step-by-step explanation:
Part a) Write an equation for T (d)
Let
d ----> the number of days
T ---> the time in minutes of the treadmill
we know that
The linear equation in slope intercept form is equal to

where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem we have
The slope or unit rate is

The y-intercept or initial value is

substitute

Part b) Find T (6), the minutes he will spend on the treadmill on day 6
For d=6
substitute in the equation and solve for T


Finding the vertex of the parabola
<span>y = (x + 5)^2 + 8 the vertex is at (-5, 8)
its coefficient so the parabola turns upward so the range is [8 , inf]</span>
You cross multiply. So 61 over 18 = x over 100. You multiply 61 and get the answer of 1600. Now with what you have left, you divide that with 18 and you should get your answer of <span>338.888889. Make sure to round it to whatever it tells you to round to!</span>