So we are dealing with reno Nevada and we have that the population Was 346.8 and that's in thousands. So 346,800 people. And this is again time is after the year, 2000 after The year 2000. And we know that in 2005 that the population was 395,000 people. And so we want to determine what K. Is and we know that the population is increasing because from 2000 to 2005 and it went up. So if we plug the 300 95 and thousands here and go through and solve for K. We'll do a Division 395 divided by that Initial population in the year 2000. And then if we take the natural log on both sides we can do a lot of power. Elena B is one and we know that this time was supposed to be five. Fuck that it should be five, this should be five. So we were just about five and that will be that's the exact value for K. Hey is approximately natural log of 395 divided by the 346 points eight. And close my parentheses. And then divide that by five. And that value comes .0-6. It continues on. But basically we know it is increasing because there is approximately a 2.6% increase per year according to that model. Then we wanted to use this model to predict and I'm just going to store that value And we want to use that model in part B to predict for 2010 And for 2015. So we'll take that initial uh huh. 346.8 times e. To the and then we'll put that docile place. But again, I'll use the start values And we'll type in 10 and we'll also type in 15 So 3 46.8 20 p. to the power of and again I'm gonna use what the value I stored the man times town and the first one comes out to be that population. We would Predict to be 400. And I'll put the actual 899, almost 450,000. and then plugging that in and plugging in 15 we get It would be up to 512,428 according to that model. And then part C said, when will it be 500,000. So when would we have this equation? And we can see it's going to happen between those two years because this came out to be a value bigger than 500,000. So I would estimate that it was going to be in 2014 but we can put that value down here and we can solve, So we would be dividing well which is gonna have that value starting my calculator. We would take the natural log on both sides. Or we could use the definition of a lot to rewrite this in the love form can move that down with a lot of the power 0.0 to 16. This is one. So it's really just dividing by that K value 10.0 to 6. So the natural log of 500 divided by that 346.8. Keeping that in parentheses and then dividing by. And again I'm going to use what I start with that value and it does say it's going to take the time of about 14 years, which means in 2014, as I had suggested it with you.