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 ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 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

Weekly Math Problem! #29

Logarithmic Equation. Y'all, it has been a loooong weekend for me. I...am...tired. 😩 Hopefully, your weekend went better than mine did. Because I'm tired and this week is a holiday week, this week's problem is a short one. Plus, I will be posting the solution earlier than usual. 

I don't encounter logarithmic equations a lot, but when I do, my eyes start to begin identifying which logarithm rules I need to use. To solve this week's problem in completion, you need to recall the following math skills:

        ✔️     Logarithm rules
        ✔️     How to solve a quadratic equation

WMP! #29 wants us to...

Happy solving!

Check back on Wednesday, November 25th for the solution, which will be posted below ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady

✏️📓 Solution Time! 📓✏️

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I won't delay. Here's how I solved the equation...

Just in case, you're wondering why x = -1 was rejected, I'll briefly explain. The domain for a logarithmic function does not include negative values. There is no exponent--positive, zero or negative) that will yield a negative result. 

Just to ensure that x = 4 won't be rejected, check it:

So, this equation has one solution, x = 4.

▪️ Comment below with your responses and let me know what you thought about this week's problem.

Thanks for solving with me this week!

Up next...WMP! #30

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Have an amazing Thanksgiving!

Cheers!

The Younge Lady

Weekly Math Problem! #10

Solving An Exponential Equation. Exponential equations are very different from polynomial equations (linear, quadratic, etc.) not just in the way they look, but also in behavior and methods needed to solve them. Exponential equations sometimes require a different type of "manipulation" via logarithmic properties, as opposed to what is needed to solve polynomial equation types, which do not require that. 

To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  Logarithmic properties

    ✔️  How to solve polynomial equations

    

I present to you WMP! #10...

Happy solving! 

Check back on Friday, July 10th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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Listen here...I looked at this problem an automatically assumed that all I needed to do was, somehow, get the exponential term in one spot--factoring it out--then I'll be good. Nah fam, not at all. 😕 When I tell you that wasn't it....that was not it. I needed another technique and wasn't quite seeing it. I was stumped for a bit. What I needed wasn't apparent to me because I was not used to using this technique to solve a logarithmic equation of this form. Factoring is what I needed to do...just not in the way I originally thought. Here's what I did:

I had to solve this thing by factoring a trinomial. It took me too long to see it. Once I saw it, it was solved in minutes. Even though, I didn't post it this week, I did check both solutions. None of them are to be rejected. 

◾️ Have you ever solved a logarithmic equation like the one above??

◾️ Comment below with your responses and let me know what you thought about this week's problem.

On to WMP! #11 ▶️

Cheers!

The Younge Lady

Weekly Math Problem! #5

Improper Integrals. A calculus thing. There's just something about solving integrals that I find very intriguing and that's probably because it requires more thought and "tricks" to get the solution, as compared to taking derivatives. But that's also the annoying thing--sometimes trying to figure out what sort of "tricks" are needed to help you figure the integral out. 🙄 

Like verifying trigonometric identities (see WMP! #3), these type of problems are also like puzzles to me. To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  Methods for solving integrals

    ✔️  Finding limits 

    ✔️  Using logarithmic rules 

It's been a super long while since I've solved an improper integral so...here goes WMP! #5... 

Happy solving! Check back on Friday, June 5th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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I don't know how much calculus you remember. I don't know how many limit rules you remember. I don't how much you remember about exponential functions. But, if you're like me, you didn't remember enough right off the top of your head to get this problem done quickly. 🤷🏿‍♀️ 🥴 

◾️ Was your solution this long?? (...Or is it just me??) 

◾️ Comment below with your responses and let me know what you thought about this week's problem.

Coming up next...WMP! #6 👀

Cheers!

The Younge Lady