All right, we know that this right here is the population growth formula were asked to find the rate of population growth, which is k constant for Arizona. Between 2000 when the population was 5,130,632 2 2006 on the population grew to 6,123,000 106. So what we need to do is plug these two values into our equation and calculate t and then solve. So why is the population we ended up with? So why is our population in 2006 and that equals Why not? Which is our starting population? Times E to the k times t now t is time. So between 2000 and 2006 that was six years. And then kay is our unknown value. So we're looking to solve for an unknown exponents, which means eventually we're we're gonna take a log rhythm. The first thing we need to do is isolate this exponential equation, and we do that by dividing by our coefficient. So we're gonna divide by 5,130,632. It this becomes one we can calculate. This is gonna be a decimal in our calculator. So six million 123,000. 106 divided by 5,130,000 632. Whoops. Try that again. 6123 106 Divided by five 130 You 6 32 Yeah, we get a value of 1.19 and that equals E to the six k now, because we haven't unknown exponents. Like I said, we need to take a log rhythm. Now we're working with E. So the base e is the natural logs we need to take. The natural log of both sides of the natural log of 1.19 equals the natural log of each of the six K. Remember taking the National League of both sides because with the equations, what you do, the ones that you have to do to the other. So on the left, we still have the natural log of 1.19 and on the right, we're gonna use properties of exponents to bring this six k down in front to multiply by the natural Aga be. So any time we haven't exploded within our longer than we can bring that down and turn it into reread it as a multiplication problem. Now, look here to simplify the natural log of e is one, so that quantity is gonna go away. And now we need to get Kay totally isolated. Right now. It's being multiplied by six. So we're gonna divide by six on both sides to solve for Kay. We're solving to the nearest tent. So we're gonna use our calculator to do this so K equals the natural audible in 0.19 divided by six. So let's go over to the natural log of 1.19 and we're gonna divide that by six, and we get a value of K of 0.28 or to nine with me. Round K equals 0.0 three. And that will be our constant population growth in Arizona between 6 4000 and 2006.