Explanation for Question 26 From the Math (Calc) Section on the Official Sat Practice Test 10
Now for number 26, we're looking at this question here, 2 which says that Keith modeled growth over 700, 3 over several hundred years of tree population by estimating the number of pollen grains 4 per square centimeter that were deposited each year. 5 He estimated that they were 310 pollen grains per square centimeter to the first 6 year. All right. So this is like our initial value and 7 the grains were deposited with a 1% annual increase. 8 It's also important that it's an increase, not a decrease, 9 um, thereafter, which of the following models function PFT after, 10 um, the first screens were deposited. And so we can see that the increase 11 here is going up by a percentage. And when your increased goes up by 12 a percentage, you have exponential growth rather than linear growth, 13 so that there is exponential. 14 And so knowing that that's exponential, we can think about the general form of 15 an exponential equation, which is a times R plus or minus or 16 rather one plus or minus R one plus or minus R raised 17 to the T or a, your initial value. 18 R is the rate and T is the amount of time, 19 right? And so we see that our initial value rate was 310 and all 20 of the equations say that. So we don't need to really worry about that 21 value. But what we can see here is that we have an annual increase, 22 right? So rather than looking at a plus or minus right here, 23 we can just go ahead and change that to a plus, because if plus 24 is indicated by an increase and a minus would indicate a decrease. 25 And now the rate that we're going up is 1%, 26 right? So 0.01 race the time. 27 And so one plus 0.01 that's 1.01. 28 And so we see that 1.01 rate here in answer choice D.