 This video will talk about exponential growth and decay rates. The percentage change in a quantity per one unit of time is called the growth or decay rate. So the base we know then should be 1 plus r. And if we solve this thing for r then we would subtract the 1 and that rate would be equal to the base minus 1. Where r, what we're looking for is a percentage written as a decimal and b is the base of the exponential function in the form of f of x equal a times b to the t since we're talking about time. So let's see how this works. Population of mice is going down exponentially per hour according to the model m of t is equal to 2 times 0.237 to the t. We know it's going down because this base is between 0 and 1. That's how we know it's going down. But we want to know according to this model what the growth rate or actually the decay rate in this case would be per hour. So remember that rate is equal to the base minus 1. And so if we have 0.237 as our base minus 1, if I call up my calculator over here, we can say 0.237 minus 1 is going to be negative, I missed it, negative 0.763. Or if we really want to know that it's negative, that means it's decay. So we don't really need to have the negative when we write the percentage. We just need to say that it's 76.3% decay per hour. So what could be a contributing factor to the success of this model? The only way I know about population of mice going down would be either traps or poison, something like that, that is going to be collecting and getting rid of our mice. Alright, so let's look at this one. An investment in a certain stock is modeled by s of t is equal to 10,000 times 1.045 where t is in years. According to this model, this base is greater than 1, so it's going to be a growth rate per year. So again, we take our base 1.045 and we subtract our 1 from it. That's going to be our rate. And these are a lot easier when you've got a base bigger than 1.045 or we could say if we move it 2 decimal places, 4.5% per year. And then it asks us how much money was originally invested. If you remember, the A or the coefficient before that base is going to be our original amount, so there was $10,000 invested. Finally, let's go the other way. Write an exponential function for the population of animals that started with 500 and is shrinking at a rate of 7.4%. So we want it to be a shrinking rate. That means that we're going to have to take our 100% and subtract off our 7.4%. Or we could think of it, we're going to need a decimal that's less than 1 since it's shrinking. We could think of it as 1 minus and convert this to the decimal already, so 0.074 and find out what that is. And if I come over here to my calculator, I can see that 100 minus 0.74 is 92.6 and I could convert that. Or if you were looking at it, it was 0.926 if I take my 1. This would be my preferred method. It's easy to convert the percentage to a decimal, and then this is going to be my base. So I start out with A is 500. So my function, P of t is going to be my 500 that I started with times the 0.926. My decay to the t.