Amazing SAT Practice but not enough Question-Specific Material

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Matthew Burgnon

2017. augusztus 4. 1:29
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I LOVE the SAT practice course. I often find myself digging up mistakes I've made and solving them to never see them again. That being said, when I run into a concept I've never learned, I struggle and find myself scouring the internet (and khan academy) to find the answer to my problem.

My most recent example of this is when I was working on the "Manipulating quadratic and exponential expressions" module and I ran into this problem:

Abhishek received an injection of a medication. The following expression shows the number of milligrams of medication left in his body after ttt hours.

37⋅0.25^(t/16)

Half-life of a medicine refers to the amount of time it takes for half of the medicine to leave the body. What is the half-life (in hours) of Abhishek's medicine?

After getting the problem wrong and reading how to solve it, I found myself confused and left still wondering why certain numbers were brought up in certain locations. Then, I looked at the videos and they apparently had nothing related to the problem I was attempting to solve (both easy and hard).

So I guess my suggestion would be to have more problem-type specific videos that can help someone like myself better learn the concepts behind some of the problems. Videos realyl are the best way I learn things so this really would help when it comes to preparing for the SAT.

Thanks for the great program and keep up the good work!

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Pei-Hsin Lin 林培心 🌸

2017. augusztus 4. 3:59

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Hi Matthew,

For help with specific problems, just post your question and the Khan Academy community will try to help you. As for the question you have mentioned:

Medicine (M) in milligrams is given as a function of time (t) in hours as follows. What is the half-life of Abhishek's medicine?

M(t) = 37·(¼)^(t/₁₆)

Just reformat the function using exponent rules, so that ½ is the base instead of ¼.

The exponent of ½ will reveal the half-life!

37·(¼)^(t/₁₆) =

37·[(½)²]^(t/₁₆) =

37·½^(2·t/₁₆) =

37·½^(⅛t)

Now that the base is ½ and the exponent is t over 8, the equation makes clear that the amount of medicine gets halved again every time t reaches a multiple of 8.

At t = 0 hours, M = 37 mg

At t = 8 hours, M = 37·½ = 18.5 mg

At t = 16 hours, M = 37·½·½ = 9.25 mg

What's the half-life? 8 hours, of course!

For more practice problems like this, check out Khan Academy's Exponential model word problems section:

https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/solving-exponential-models/e/exponential-models-word-problems

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Amazing SAT Practice but not enough Question-Specific Material

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