The increased above the normal risk risk of having a car acc

The increased (above the normal risk) risk of having a car accident increases exponentially as the concentration of alcohol in the blood increases. The risk can be modeled by R=9e^12.77x (for x > 0) where x is the blood alcohol concentration (BAL) and R, given as a percentage, is the increased risk of having a car accident. Show work for all calculations and give concise explanations to both questions. a) In the state of Florida, the legal blood alcohol level (BAL) is 0.08. Find and interpret the meaning of BAL.=.08. Give the answer rounded to two decimal places. b) Find and interpret the meaning of R=50. Give the answer rounded to two decimal places.

Solution

(a) We have R = 9e^12.77x. Thus, when x = 0.08, R = 9e^12.77*0.08 = 9e^1.0216 = 9*2.777635427 = 24.99871884 = 25 % (on rounding off to 2 decimal places ). It means that there is a 25 % risk of having a car accident when the blood alcohol level (BAL) is 0.08.

(b) When R = 50, we have 50 = 9e^12.77x or, e^12.77x = 50/9. On taking natural logarithm of both the sides,we get (12.77x) ln e = ln (50/9) or, 12.77x = ln 50 – ln 9 = 3.912023005- 2.197224577 = 1.714798428 = 1.71 ( on rounding off to 2 decimal places). It means that there is a 50 % risk of having a car accident when the blood alcohol level (BAL) is 1.71