Explanation for Question 29 From the Math (Calc) Section on the 2019 October Sat
Now in question number 29, we're told about a cup of hot chocolate. 2 That's placed in a room that's 70 degrees, 3 and it starts out at 180 5. And then we're given a bunch of different 4 functions here that we can use this information to show how the temperature 5 of the cup of hot chocolate changes. And so you might be tempted to 6 try to take these numbers that were given and turn them into an equation, 7 but what's probably the best way to solve this problem. 8 And most efficient, since you have use of a calculator is going to be 9 to take some of the data points that were given here. 10 And the later part of the question with the temperatures and the time, 11 and then plug them into some equations and see which one actually gives us 12 the right values. However, 13 there is one equation that we can eliminate right off the bat. 14 And that's going to be answer choice a, because we noticed that a has 15 a 1.25 and the spot where you put the rate for exponential growth, 16 right? So we talk about growth, um, exponential. 17 We can think about the general form of equation, 18 a to the R a times R to the T where ours, 19 your rates. And if you're growing, 20 your R is greater than one. And if you're, 21 um, getting smaller decreasing, 22 right, your ours less than one. And we know that, 23 um, the hot chocolate is decreasing. 24 Temperature is cooling down. So that means our, 25 our would have to be less than one. And since ours greater than one 26 and can be eliminated right ...