The concentration of alcohol in a person's bloodstream is measurable. Suppose that the relative risk R of having an accident while driving a car can be modeled by an equation of the form R=e^kx where x is the percent of concentration of alcohol in the bloodstream andk is a constant. Suppose that a concentration of alcohol in the bloodstream of 0.03 percent results in a relative risk of an accident of 1.4. Find the constant k in the equation.

Alonzo Odom

Alonzo Odom

Answered question

2022-07-20

The concentration of alcohol in a person's bloodstream is measurable. Suppose that the relative risk R of having an accident while driving a car can be modeled by an equation of the form R = e k x where x is the percent of concentration of alcohol in the bloodstream andk is a constant. Suppose that a concentration of alcohol in the bloodstream of 0.03 percent results in a relative risk of an accident of 1.4. Find the constant k in the equation.

Answer & Explanation

Kyan Hamilton

Kyan Hamilton

Beginner2022-07-21Added 12 answers

To solve the problem, substitute the given values of x and R in the given equation and solve for the value of k.
1.4 = e 0.03 k Rewrite in natural logarithmic form.
0.03 k = ln 1.4 Divide both sides by 0.03
0.03 k 0.03 = ln 1.4 0.03
k = 0.3365 0.03
k=11.22
Thus, the value of the constant k is 11.22
Result:
11.22
Jadon Melendez

Jadon Melendez

Beginner2022-07-22Added 4 answers

Substitute 0.03 to x and 1.4 to R in the given equation to find the value of k:
R ) = e k x
1.4 = e k ( 0.03 )
1.4 = e 0.03 k
Use the rule a = e b ln a = b to obtain:
ln 1.4 = 0.03 k
ln 1.4 0.03 = 0.03 k 0.03
ln 1.4 0.03 = k
Use a calculator to obtain:
k=11.21574122
11.2157
Thus, k = ln 1.4 0.03 11.2157
Result:
k = ln 1.4 0.03 11.2157

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