[Video] Q28: In planning maintenance for a city’s infrastructure, a civil engineer estimates that, starting from the present, the population of the city will decrease by 10 percent every 20 years. if the present population of the city is 50,000, which of the following expressions represents the engineer’s estimate of the population of the city t years from now?

Explanation for Question 28 From the Math (Calc) Section on the Official Sat Practice Test 3

So now we're looking at question number 28, which says that in planning, 2 maintenance for cities, infrastructure, we're estimating that we're starting. 3 Um, the city will decrease 10% every, 4 uh, 20 years, right? So we're decreasing by 10%, 5 every 20 years. And the present population is 500,000. 6 And so we're trying to model model this growth, 7 right? And so we need to think about the equation for exponential growth and 8 its general forum, which is Y is equal to a times, 9 our race to the T where a is your initial amount are, 10 is your rate of either growth or decline. 11 And then T is your time, the time interval for one of those, 12 um, periods of growth, right? And so we should immediately see if we're decreasing 13 by 10% decreasing by 10%. 14 Then our rate has to be less than one because a decrease has a 15 rate that is less than one, whereas increase has a growth rate, 16 right. 17 Greater than one. And so if we're decreasing by 10%, 18 we need to be less than one by 0.1, 19 which we see here with the 0.9. 20 Right. And then we need to think about, 21 okay, well what goes in my exponent? Is it T 20 times T or 22 T over 20? And so we see right, 23 that one, um, period of growth is 20 years. 24 That's one growth period. And we're asking in terms of T years, 25 right? And so I know that I'm going to be multiplying, 26 um, by one for, 27 well, let me restate that over a period of 20 years, 28 I would have only decreased by 0.91 time, 29 right? Because it takes those...