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Interpreting nonlinear expressions — Harder example

Watch Sal work through a harder Interpreting nonlinear expressions problem.

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• I have my SAT tomorrow and I am reviewing some math. How is 64 distributed. I know you explained this in a previous comment, but if you look closely, d is not being distributed. Therefore, if you are multiplying d by 64, why is it necessary to distribute every number by 64 if it was not original apart of the distributive property.
• If 4d^3 = (4^3)(d^3), then it amounts to 64d^3. 64 is distributed because the equation is 3.98*10^-20*64d^3. All terms are being multiplied by 64, so it can be factored. Sorry that your question wasn't answered until now! :(
• Doesn't factoring out the 64 imply that the the 64 is multiplied by every term in the parentheses?
• You don't have to do this in this specific case because we just have to see how many times longer Mar's revolution time would be compared to that of Mercury's. We just have to see that one value which shows how much longer the revolution would take (8). Multiplying 64 with every single term in the parentheses (after finding the principal root which is done near ) would just add an extra step. Remember, the SAT is time constrained, so the quickest option should be used!
• Isn't 6% 0.06? Then why did you consider that it is 1.06 in Interpreting nonlinear expressions — Harder example?
• 6% is indeed .06, but that's not all the question asks you for. Instead, the answer choices describe "an increase of 6%". To put that into math, it's the original price plus 6% of what it was:
x + .06x = x(1.06)
That's how we get 1.06 for the 6% increase, and why it's in there instead of plain .06. If the function was 10000(.06)^(q/4), it would mean that the styling service only retains 6% of its subscribers per year, or that it loses 94% every year.
• Hi! I have a question... I don't understand how you would square root the whole equation after you substitute the number 4 into d (for distance)? Can someone please explain it to me? Thank you in advance! xx
• Can anybody explain me that q/4 how its not 1 quarter? I am utterly confused
• If we have q = 1 it means it is one quarter. When it is q = 4 its is one whole year as in one year we have 4 quarter
• For those who do not understand why q/4 is not 4q.
First, q/4--
We all know that q is a quarter year. Right? In 4(1.01)^q/4, the reason why we want to make q/4 is that we want to make the degree of 1.01 one. Meaning, 4 quarters are equal to 1 year. So the degree is 1 and 4(1.01) ^4/4 = in one year the number is increasing by 1 percent.

Second, if we do q*4 then--
4(1.01)^4q imagine we want to find the yearly increase. What do find here then? Okay 1 year=4 quarters, put it. 4(1.01)^4*4. See the degree is not one.

Well, additionally. We need 4 circles. We cannot do it by 4q but q/4.
• At when 1000(1.06) and 1000 is increasing by (1.06). Why is it increasing by 6%, and not 106%? Where does the 1 away from (1.06) go?
• 1.06 -> 106%
106% - 100% = 6% > 1 (increasing)
• Is there any other way to solve this problem without having to make a T-chart?
• Hi Rachel!
I think the best way is elimination. Since we know we have an exponent in the equation, we know we have an exponential function which means that it's not increasing by a certain amount each year but rather by a certain factor. (Eliminate a and b). To increase by 6% we need to make sure that 1.06 is only raised to the first power. That means q must equal 4 since 4/4 = 1. q equaling 4 means that that's four quarter years. What's four quarter years? 1 year.
I know that maybe looked long and hard, but when you do it in real life, it takes much less time than Sal's way.
• What kind of topics are there in sat
• The Math SAT has 3 major categories: Heart of Algebra, Problem Solving and Data Analysis, and Passport to Advanced Math.

See the CollegeBoard website for a more detailed explanation.