For the first question in Tickbox 6, regarding the corresponding image, why does Greg state that there isn’t enough information to determine the value of f(5)? It seems that in the previous cases, x is squared, so f(5) should clearly be 25. What other possibilities could there be?
As for question 20, based on the image provided, can we set up two equations: “1 = 15 * r * 12” and “1 = (15 + x) * r * 10”? If we divide these equations, we arrive at 150 + 10x = 180, leading to x = 3. (I know the answer is 3, but I wanted to verify the logic of this alternative approach. Is it correct?)
Additionally, why do we express the interest rate as a decimal (e.g., 12% as 0.12) in the compound interest formula, while in the simple interest formula, we use it as a whole number (e.g., 12)? In the compound interest calculation, we divide 0.12 by 1 (once a year), but in the simple interest formula, we use “12” in the expression prt / 100 ??
Also, could you clarify what is meant by “to the nearest second” and “to the nearest minute”? Does “to the nearest percent” refer to rounding to the nearest hundredths?
For compound interest you have A = P (1 + \frac rn)^{nt} - P, where r is rate in decimal. The same thing holds for simple interest I = Prt where r is again the rate in decimals.
Replace “to the nearest” with “round”. Maybe it’s more clearer what “round to the nearest minute” means.
For example, 5.13 minutes to the nearest minute is just 5 minutes because rounding 5.13 to the nearest minute is equivalent to rounding to the nearest whole number, which is 5.
Firstly, thank you so much for your detailed responses!
Secondly, regarding the first question about f(5), we can identify a pattern since f(2) = 4, f(3) = 9 , f(4) = 16. It seems f(x)= x^2 , so f(5) would be 25.
Thirdly, regarding compound and simple interest formulas, the flashcard states that I = Prt / 100 for the simple interest. The division by 100 means we don’t need to convert to decimal form, right? However, this doesn’t apply to the compound interest formula since it doesn’t include “100,” requiring us to use the decimal. Please correct me if I’m wrong.
Lastly, could you clarify whether “to the nearest percent” means rounding to the nearest hundredths?
I’ve already answered this. Check the function i typed out for you above and evaluate it at x = 2,3,4, and 5. Specifically, see what f(5) evaluates to.
Okay, so the “r” here is in percents. But if you define a new variable R such that its r/100 then your new formula would be I = PRt. Notice now the R is in decimals just like in your compound interest formula.
In a similar fashion, if you don’t like the fact that r is in decimals in the compound interest formula, you can redefine a new variable such that the rate is in percents. It’s all trivial and i don’t think it needs much attention.
Also, already answered this. It’s rounded to the nearest whole number.
For example, 5.13% rounded to the nearest percent would be 5%.
I’ve got a good grasp on the f(5) question, thanks!
For the compound and simple interest calculations, I plan to use their standard formulas with decimals, as dividing by 100 can be confusing.
Regarding the last point, I thought you had addressed the issue of minutes and seconds. However, I’ve noticed that when it comes to “rounding to the nearest percent,” sometimes if the value is 0.33, the result is simply recorded as 33% without rounding (not 30%). This made me think there might be a difference compared to rounding for seconds and minutes.
Yeah, well it doesn’t matter what u use as long as the “result” makes sense. For example, if you used rate as a decimal in your flashcard formula then the interest would appear pretty small. That should be a good “check” to see if the result makes sense. If not, you can just make a formula for both which uses either decimals only or rate.
0.33 is the decimal representation of a percent. 0.33 is 33%, right? 33 is a whole number so there’s no reason for u to round to 30%.
Another example could be 0.335. First, you translate this decimal into an equivalent percent by multiplying by 100 to obtain 33.5%. Now rounding this to the nearest percent would give 34%.
Thank you so much for your help! For the final round, could you please rewrite the formulas for compound and simple interest? I encountered a “MATH PROCESSING ERROR!” in the previous messages, and I couldn’t see them.
I remember that the formulas I received were slightly different from what’s shown in the flashcards. So, if the question states a 12% interest rate, we should use 0.12 in both formulas, correct?
I just want to confirm this for the final time. Thank you!
For simple interest, if you want your rate in percents (like in your flashcard) then you’d use:
I = \frac{prt}{100}
but if you define a new variable like so: R = \frac{r}{100} then your new formula would be
I = pRt, where R is now evidently in decimals. \rule{20cm}{0.4pt}
For compound interest, a similar thing follows:
I_C = p \left( 1 + \frac rn\right)^{nt} - p
In the above case the rate is in decimals, but if you want it in percents then just define a new variable \left(r = \frac{v}{100}\right) and replace like so:
I_C = p \left( 1 + \frac{v/100}{n}\right)^{nt} - p = p \left( 1 + \frac{v}{100n}\right)^{nt} - p, where v now represents the rate in percents.
Tldr;if you have it in decimals then you can define a new variable such that it takes in percents and divide that by 100. The reverse also holds equivalently.
In your flashcard formulas, no. The simple interest formula uses r as percents, while the compound interest formula uses r in decimals.
But from my above message, you should be able to quickly make a formula such that both are in percents or both are in decimals. Actually, you don’t even have to make it cuz i already did it for you, but hopefully that made sense.
