Question

How does the blood alcohol concentration affect the likelihood of getting into a car accident

while driving?

According to medical research, the risk of getting into a car accident increases exponentially as

your blood alcohol concentration increases.

The risk is modeled by the equation R = 6e¹2.77x, where "R" is the percent chance of the risk

of having a car accident and "x" is the blood alcohol concentration.

a) First graph this function on a calculator and sketch it here with a domain of [0,0.3] and a

range of [0,100]

Answer 1

Answer:

See attachment.

Step-by-step explanation:

Given function:

$R=6e^{12.77x}$

Given parameters:

• Domain: [0, 0.3]
• Range: [0, 100]

The y-intercept is when x = 0:

$\begin{aligned}x=0\implies R&=6e^{12.77 \cdot 0}\\R&=6\end{aligned}$

Locate more points on the curve by inputting different values of x from the given domain:

$\begin{aligned}x=0.05\implies R&=6e^{12.77 \cdot 0.05}\\R&=11.4\;\; \sf (1\;d.p.)\end{aligned}$

$\begin{aligned}x=0.1\implies R&=6e^{12.77 \cdot 0.1}\\R&=21.5\;\; \sf (1\;d.p.)\end{aligned}$

$\begin{aligned}x=0.15\implies R&=6e^{12.77 \cdot 0.15}\\R&=40.7\;\; \sf (1\;d.p.)\end{aligned}$

$\begin{aligned}x=0.2\implies R&=6e^{12.77 \cdot 0.2}\\R&=77.2\;\; \sf (1\;d.p.)\end{aligned}$

Find the x-value when R = 100:

$\begin{aligned}\implies 6e^{12.77x}&=100\\e^{12.77x}&=\dfrac{50}{3}\\\ln e^{12.77x}&=\ln \left(\frac{50}{3}\right)\\12.77x \ln e&=\ln \left(\frac{50}{3}\right)\\12.77x &=\ln \left(\frac{50}{3}\right)\\x &=\dfrac{\ln \left(\frac{50}{3}\right)}{12.77}\\x&=0.22\;\; \sf (2 \; d.p.) \end{aligned}$

To draw the graph:

• Use a scale of x : y = 1 : 400.
• Plot the y-intercept at (0, 6).
• Plot points (0.05, 11.4), (0.1, 21.5), (0.15, 40.7), (0.2, 77.2).
• Plot point (0.22, 100).
• Draw a curve through the points.