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(See Week 1 Lecture page "The Equation of a Line 1" for a starting point.
25. (See Week 1 Lecture page “The Equation of a Line 1” for a starting point.)
As part of the second stage of a drug trial, volunteers are given one of two dosages, in order to determine therapeutic levels. Volunteers who were given 6.5 mg had blood concentrations of 2.7 parts per million (ppm), while volunteers who were given 10 mg had blood concentrations of 5.1 ppm.
a.) Determine the equation of a line that models this data, where x is the dosage given and y is the blood concentration.
The equation of line 1
points: (x, y) = (6.5, 2.7) and (10, 5.1)
Use the point slope equation
y – 2.7 = 5.1 – 2.7 / 10 – 6.5
y = 24/35 (x – 6.5) + 2.7
y = 24/35 x – 123/70
Graph this line. (I already have the line graphed)
c. If the desired concentration in the bloodstream is 7.5 ppm, what should be the therapeutic dosage?
y = 7.5
24/35 x – 123/70 = 7.5
⇒24x/35 = 7.5 + 123/70
⇒ x = 324/35 * 35/24
⇒ x = 13.5mg (Now I need the therapeutic dosage.)
d. If the toxic concentration in the bloodstream is 11.8 ppm, what is the maximum safe dosage?
y = 11.8
⇒ 24/35 x – 123/70 = 11.8
⇒ 24x/35 = 949/70
⇒ x = 949/70 * 35/24
x = 19.77mg (I need the maximum safe dosage as well.)
I have some of the answers but my question is can someone explain the steps as to how the answers were generated or how you came up with the answers? Also, there are parts left out. So, can someone answer d) if the desired concentration in the bloodstream is 7.5 ppm, what should be the therapeutic dosage. If the toxic concentration in the bloodstream is 11.8 ppm, what is the maximum safe dosage.(Would you explain, briefly how you found the slop on part a) and give the slope formula you used to find the slope?)
