Explanation for Question 28 From the Math (Calc) Section on the 2019 March Sat
Question 28 says the wholesale price of a kilogram of lentils decreased 2 by 1% from the previous month for six consecutive months. 3 If X is the number of months since the price began to drop. 4 And why is the cost of a kilogram of lentils, 5 which of the following equations could model the cost of lentils over this time 6 period. So to start off, 7 we can eliminate answer choices a and B right off the bat. 8 And that's because this isn't a linear equation, 9 it's an exponential equation. And we know that because the amount that the price 10 of the lentils is changing by isn't consistent. 11 It's not constant. It depends on the previous value of the lentils. 12 The amount of changes changes every single month. 13 And so it can't be a linear function. It has to be an exponential 14 function. Now, when you're dealing with exponential functions, 15 this is typically the formula that you should use. 16 Y is equal to a times one plus or minus R to the value 17 of T where a represents the initial value. 18 So in this case, that's the initial price of the lentils. 19 And in both possible answer choices, 20 that's 1.65, then R represents the rate of increase 21 or decrease in this case, the price of lentils is decreasing. 22 Um, so we're going to do one minus R and then T is the 23 amount of time which in this equation is represented by X. 24 So since the number of, 25 or the price of the lentils is decreasing in this function, 26 we're going to use one minus R and R is equal to 1%, 27 which means that we're doing one minus 0.01. 28 And so in the parentheses should be 0.99. 29 And so that's how we know the answer here.