Explanation for Question 15 From the Math (No Calc) Section on the 2020 March Sat
So question number 15 is asking us for the half-life of a certain substance 2 being 150 years, 3 right? So the amount of time that it takes for this substance, 4 for that amount to be cut in half is going to be 150 years. 5 And the question is asking us, which of the following exponential functions, 6 models, the amount in grams two years with the starting amount 7 of 200 grams. Right? And so our answer choice tells us that the correct 8 answer is deep. And the reason that the correct answer is going to be 9 D is because it shows us the correct starting amount. 10 It has the correct timeframe. Um, 11 and it has the correct numbers in the exponent as well, 12 right? Because if we look right here, we can see that they tell us 13 that we start with 200 grams of the substance. 14 And so that's why we want to have a 200 right here rather than 15 the one 50. 16 Because if we think about the exponential growth function, 17 it's our amount, Y is equal to our starting amount, 18 a times, our rate raised to the amount of time, 19 right? So we're a, is your initial amount. 20 So since we started with 200, it has to be either C or D, 21 right? And now the reason that the one half is here is because we're 22 talking about a half-life right. 23 We're cutting the amount in half. So that's our rate, 24 50% or one half. Now the difference between C and D is the time 25 what we have in our exponent. 26 And what we know this needs to be right is the 27 amount of time, or I guess the amount of c...