In this video, we will work with exponential growth using the rule of 70. The doubling time or the rule of 70 can help determine the number of years it takes for a population or an investment to double. To find the doubling time, a quantity growing at a given annual percentage rate, for example, 10%. So if I have 10% growth rate, um you divide 70 by the percentage to determine the doubling time. So in the case of 10% you would take 70, you divide by 10 and 70 divid by 10 is seven. So if you have a 10% growth rate of something, it would take seven years for it to double. In this problem, it reads, "If the population of rabbits and an ecosystem grows at a rate approximately 4% per year, the number of years required for the rabbit population to double is closest to, and here are some choices." So, let's see how we can solve this problem. All right, let's take a look at the equation before we do that. So, here's a couple sample equations. Here's the um 70% divided by the number of years to double. And so, let's do some sample problems before we go to the real problem. And how many years would it you expect the population to double if the population growth rate is 2% per year? So in this case you would take 70 divide by two and 70 divid by two is 35 years. So if you have a 2% growth rate it would double in 35 years. In the second problem we have uh five years for a population to double. Determine the constant rate growth. So this is a little different kind of a problem because it's trying to solve for the um percentage. So you could say 70 divide by p and that equals 5. And when you're trying to solve this problem, you can cross multiply. Think of the five is 5 over 1. And if you recall from mathematics, if you cross multiply equivalent fractions, they're the same. So you can say 5 * p or 5 p would be equal to 70 * 1, which is just 70. Now to solve for P, you would divide both sides by five, right? So the five cancels and you get P. So you get a calculator out or something like that and we take 70 divided by five, you get 14. Oops, I'm not writing it correctly. 14%. So the growth rate of something that doubles every 5 years, well that would be 14%. So now let's go back to the original problem. The original problem says we have these um rabbits in the ecosystem and they grow at 4% per year. So we're going to take 70 and we're going to divide by four because this is our percentage, right? 4% growth rate. And when you take 70 by divide by four, get your calculator out. That comes out to 17 and a half. Well, 17 and a half, of course, is closest to letter D, 17 years.