Question

50 = 6e ^ 12.77x

Answer 1

What is the question? Solve for x?

Answer 2

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 3

so yes , basically solve for x

Answer 4

take natural log on both sides

Answer 5

ln ?

Answer 6

yes

Answer 7

ln e = 1

Answer 8

Divide both sides by 6. Then take ln on both sides.

Answer 9

oh yes

Answer 10

so i divide by 6 first ?

Answer 11

yes.

Answer 12

do i leave is as a fraction or convert into a decimal ?

Answer 13

what does e mean anyways ?

Answer 14

For mathematics, it is good to get into the habit of leaving it in its exact form (fraction/rational). Decimals are merely approximations and are usually reserved for sciences. So for math, unless you are explicitly told to put in decimal form, leave it in fractional form.
Also,
\(e^n\)
this is Euler's number I believe is its name. \(e^1\) is like 2.7 something, it is kinda like \(\pi\).

Answer 15

ok thank you but may you guide me through solving the rest of the problem please ?

Answer 16

@austinL

Answer 17

Okay, we have

\(\displaystyle 50=6 e^{12.77x}\)

First I would divide by 6 to get the \(e\) by itself.

\(\displaystyle \frac{50}{6}=e^{12.77x}\Rightarrow\frac{25}{3}=e^{12.77x}\)

Then you would do as @hartnn said, you would take the natural log of each side.

\(\displaystyle \ln(\frac{25}{3})=\ln(e^{12.77x})\)

\(\displaystyle \ln(\frac{25}{3})=\cancel{\ln}(\cancel{e}^{12.77x})\Rightarrow\ln(\frac{25}{3})=12.77x\)

Do you think you could solve it from here?

Answer 18

ln cancels out with e ?

Answer 19

The natural log does indeed cancel out the e.

Answer 20

all the time ?

Answer 21

ok so when do i know that i will need to take the natural log of each side ?

Answer 22

If you have an x in the exponent of an \(e\). You will do that to get it down so that you can solve for it.

Answer 23

ok thank you so much , i have another question but i will post a new one , can you help me on it as well ?

Answer 24

Sure :)