Explanation for Question 16 From the Math (Calc) Section on the 2020 October Sat
So number 16 is asking us to choose the function that best shows what's 2 happening in the paragraph. And if we read the paragraph, 3 we can see that at the beginning of the study, the initial population of 4 bacteria is, is a 150,000. 5 And then we go on to see that the bacteria doubles every hour. 6 Now, when something doubles every hour, 7 that's a sign that this is exponential growth, 8 exponential growth, and that it's not linear growth. 9 So we want to choose a, an equation that shows us exponential growth. 10 And it looks like all of these are kind of in that category, 11 although C and D look a little bit different, right? 12 And then we read on for a limited time, which equation, 13 best models, um, the bacterial growth. 14 Now, whenever we have exponential growth, the format that we want to follow is 15 shown in a and B, or we have, 16 Y is equal to a X X 17 a times. 18 Your rate raised through a time where ours, 19 like your rate of growth, how fast you're growing T is time in a, 20 is your initial to model exponential growth. 21 You don't use a parabola, right? 22 And C and D have an X squared term. These are parabolas. 23 And so that's why C and D are going to be wrong. 24 So now looking between a and B, we have to decide, 25 should the rate, should the doubling go in the exponent or down from the 26 exponent? And if we look again at this, 27 uh, this general formula that we use for exponential growth, 28 the rate is a normal number that is raised to the time. 29 The rate is not in the exponent as that's why B is going to 30 be our best answer.