Question

Use the formula R = 6e12.77x, where x is the blood alcohol concentration and R, as a percent, is the risk of having a car accident. What blood alcohol concentration corresponds to a 50% risk of a car accident?

Answer 1

`R=6e^(12.77x)`

`50=6e^(12.77x)`

`(50)/(6)= e^(12.77x)`

`log (50)/(6)=log( e^(12.77x))`

`0.920818754=12.77x`

`x=0.07`

Answer 2

0.1660 ( approx )

Explanation:

Given,

The percentage of risk of having a car accident is,

`R=6e^(12.77x)----(1)`

Where, x is the blood alcohol concentration,

From equation (1),

`(R)/(6)=e^(12.77x)`

Taking natural log both sides,

`ln((R)/(6))=ln(e^(12.77x))`

`ln((R)/(6))=12.77xln(e)`

Since, ln(e) = 1,

`ln((R)/(6))=12.77x`

`\implies x = (ln((R)/(6)))/(12.77)`

R = 50 %,

`\implies x=(ln((50)/(6)))/(12.77)`

`=(2.1202635362)/(12.77)`

`=0.16603473267\approx 0.1660`