[Video] Q23: M = 1,800 1.02 ^t the equation above models the number of members, m, of a gym t years after the gym opens. of the following, which equation models the number of members of the gym q quarter years after the gym opens?

Explanation for Question 23 From the Math (Calc) Section on the Official Sat Practice Test 8

So question 23 gives us this entire equation here, 2 but the focus of the problem is not the whole equation, 3 rather the exponent T. And so we're told that we're trying to take this 4 to you, which is in years, I figure out how we could convert it 5 into quarters. And when we convert the time from your supporters, 6 we're not actually going to change the rate. We look at C and D. 7 These both change the rate. So C and D has to be wrong because 8 this needs to be 1.02 it's. 9 Now, if we think about how we can convert years into quarters, 10 we know that there are four quarters in a year, right? 11 So four times the number of years will give us the number of quarters 12 and that's acute. And we know that our time T is in year. 13 So I can take this year's aspect that I've written down and replace it 14 with a T instead. So 14. 15 And now if I'm solving for T right, cause I need to take whatever 16 I have and plug it in for tea up here. 17 All I can divide both sides by four and I get the quarters over 18 four is equal to T so essentially I can take this whole Q over 19 four and plug it in for my exponent up here. 20 Now a has the Q over four. So our best answer is going to 21 be a.