Medical research indicates that the risk of having a car accident increases exponentially as the concentration of alcohol in the blood increases. The risk is modeled by
R=6e^12.77x
Where x is the blood alcohol concentration and R, given as a percent, is the risk of having a car accident. What blood alcohol concentration corresponds to 20% risk of a car accident?
done, see below, please don't switch names
To find the blood alcohol concentration corresponding to a 20% risk of a car accident, we can use the given equation: R = 6e^(12.77x), where R is the risk and x is the blood alcohol concentration.
We need to solve for x when R is equal to 20%. To do this, we'll set R equal to 20 and solve for x.
20 = 6e^(12.77x)
Now, let's isolate the exponential term:
e^(12.77x) = 20/6
Next, take the natural logarithm (ln) of both sides to eliminate the exponential:
ln(e^(12.77x)) = ln(20/6)
Using the property that ln(e^a) = a, the equation becomes:
12.77x = ln(20/6)
Now, divide both sides by 12.77 to solve for x:
x = ln(20/6) / 12.77
Using a calculator, the value of x is approximately 0.1008.
Therefore, a blood alcohol concentration of approximately 0.1008 corresponds to a 20% risk of a car accident.