Weekly Math Problem! #36

Exponential Application. Math makes the most sense to me when it has a real-world application. (Oh how is wish theory made more sense to me.) So, every now and again, I like to get word problems in. (**Whispering** But that doesn't mean I love word problems. I still find them scary sometimes.) 

This week's problem is very relatable to everyday life. What is the likelihood that you (as the driver) will get into an accident with a certain blood alcohol level? It makes sense that the more intoxicated you are, the less alert you are, making it easier for you to get into an accident. (That's the best way I could say it, although there is probably a more accurate way to express this.) To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     How to solve an exponential equation
        ✔️     How to isolate the exponent in an exponential equation

WMP! #36 says:

See problem here.

Happy solving!

Check back on Friday, February 5th for the solution, which will be posted below ⬇️.

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✏️📓 Solution Time! 📓✏️

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Let me just start with where I went wrong in solving this problem. 😕 Here is what I did initially:

Can you see what the problem is? It isn't the steps I used that are incorrect. It's the answer I got. When I saw that the answer was negative, I felt like something was wrong. So, the first thing I did as go back over my solution to see if there was an error in the computation. I didn't find anything. Next, I decided to plot the function to see what the curve looked like. Hmm... 🤔 The curve looked fine to me but, when I plotted the risk from the problem with the corresponding blood alcohol concentration (BAC) I solved for, it further confirmed that a negative answer wasn't it. I quickly looked up BAC numbers and was informed that in the US, they should be positive ranging from about 0.08% (0.0008) to 0.40% (0.0040). Okay.

Then, I went back to the word problem and read it again to see what it said. (...And this is why word problems aren't my friends.) The problem said "R is a percent." Noticed I let R = 0.25. Why? I am so used to converting a percent to its decimal representation when working with exponential equations, that I was so sure R should be 0.25 instead of 25. 🙄 I read that thing and didn't even think that R should be a whole number. 🤷🏿‍♀️ Here is my corrected calculation:

According to this model, the BAC that corresponds to a 25% accident risk is approximately 0.11% (0.0011). *The problem didn't say what the unit for BAC is. Now that I am more familiar with it, I know not to convert the 0.11 to 11%.*

This problem definitely had me do more work that I thought I would. No worries. I won't stop solving...and neither should you. 

▪️ How much did you know about BAC?

▪️ How did you find this week's problem?

▪️ Leave your response down below and let me know what you thought about this week's problem.

Thanks for solving with me this week!

Onward to WMP! #37

Cheers!

The Younge Lady