All right. So for this one, Number seven, we're talking about population growth. And what is asking for, uh, Teoh come up with a formula for the population of for the girls of the population in the city within a certain timeframe. So this is the general formula for population growth, which is, and of tea, final amount, Ingles and subscript Oh, in this hole, he's constant. Okay, is growth rate and t is time. All right, so for B, it's a two step problem. So they give us the initial amount. The initial mount is 10,000. Okay, Now it says after 18 months, it's going to hit 20,000. So 18 months equals 20,000. Well, it isn't 20,000. Exactly. They're saying that the population will double in 18 months. 10 times two is 20,000. All right, so we have that we don't have is the rate we don't have K. I am. We need cane or to figure out the rest of the problem because then what it's asking for is they're saying, How big will the population get after two years now? Two years? There's 12 months in a year, right? So 12 times two equals 24 months. So 24 months. So how big will the population get in 24 months Now? We can't solve this until we get the rate. So that's sulfur. The rate. So 20,000 equals 10,000? Yeah, to the K. And then T is 18 months. All right, so let's get another color. Divide the 10,000 now. You should get to equals e. Okay. 18 Ah, Ln two. Which cancels out the e que 18. So why not the 18? And you should get k equals roughly around, um 0.385 Now, if you plug Kate, this the rounded form into the equation, um, you're going You're not going to get what it says in the book. So here, I'll show you both ways. We just school up school too much, OK? No, that's not what I know. It's not what I want, Okay? They really All right, So that's plug it in since we have the rate. So we're trying to find on this key, and we start off a 10,000 E to the 0385 times 24 months. Now. When you put that in the calculator, you should get around 25,000 193. That's how much will be after 24 months about now. If you if you saw for K and you put the exact amount, which is K equals 0.385 081 and it keeps going going. So we just, you know, copy and paste that into your calculator and put it here. Then you'll get what the book says, which is 25,000 198 and that's it for this problem.