Explanation for Question 20 From the Math (No Calc) Section on the 2020 October Sat
So now we're onto question 20, which is the final question of the math, 2 no calculator. And we see that we're given a collection of data right here 3 and I still table. And then we're given this expression, 4 right? Or equation F of X is equal P R X. 5 We know that PNR are constant. So that means they'll stay the same, 6 no matter what the value of X is. And we need to know the 7 value of R. Now the tough thing about this one is that there's two 8 variables here, right? We know X we're given all the exes and we're given 9 all the F of is, but we don't know P and we don't know 10 R so that means if we're solving for are a good, 11 first step is defined. What is key that way we have all of our 12 other variables accounted for. And the way to do that is going to be, 13 to use this point. 14 And I see the F of zero is equal to P times R to 15 the zero power. Now F of zero is nine P we're searching for it. 16 And we can ask ourselves, what is our to the zero with power. 17 Now, anything raised to zero is always going to be one. 18 So the reason that this point is useful to us is because it kind 19 of gets rid of the R the R that's in the way and allows 20 us to solve for P. So what times one is equal to nine. 21 That means key is going to have to be equal to nine. And this 22 might not seem useful at first, because if we didn't solve for R yet, 23 but we can use that value of P to write a second equation. 24 Very similar to the first, just using a different data point where we so...