So for this given formula, we need to draw the second secret line. Who Slope is average rate of change and infected children over the intervals for six and 12 14 than compute these average rate. So what we'll do is basically a secret line. Is the line drawn between two points? So let's do that for this first interval here or on the Y axis. Let's let's to note that as a point, which is right here and then for six, our wise air here. So we will draw online in between these two points on DH. Then let's do the same for 12 and 14. So 12 is right here. That's it's why and then 14 is right here. That's it's why and so its secret lines from right here. Great. And now let's compute each of these average rates in units of percent per day. So for six, what were simply doing is we need to find the co ordinates before we plug it into a rate of change formula, and the way we do that is we simply plug in these exes back into this function, so when I do that, you should get a value of 12 white, 903 and then for six. It's why coordinate is 20 point or 55 perfect. And now let's plant that into a rate of change equation, which is change of why we're changed bags. And I'm just going. Teo put a green box to help me organized on DH. Now I will subtract both of these y values. So 20 point for by five minus well, 0.9 au three all over six minus six minus four. And what you should get is 3.776 percent per day. That's your answer for the first part of a part. Ay, for the second part, Um, what I'm going to do is always the same exact steps for the interval. 12 14 on DH. When I plug in these X values back into the function to Courtney Hits I get is okay. So for 12 I have eaten point A for five, and then for 14 I have 14. I have, um, 7.2 for nine. And let's plug that into this equation to get our rate of change. So seven point two for nine minus and 0.8 for five all over um 14 minus 12. And he should get a rate of negative 0.798 percent a day. And that is the second answer for part A. So, for part B is a rate of decline. Greater At T equals eight er t equals 16. So what I will do for this part is I'm actually going. Teo, change the color. Let's see if this works this time. Great. So, um, a T equals a What I'm going to do is actually draw a tangent line. Um, in order to help me count Ilia rated change, whether it declines faster, and the steeper it is, the greater the rate of decline. Um, so I'm going, Teo, a race a little bit of this point in orderto make way for Actually, I'll leave it as is, so that we have this visual s o for a We can draw point here. Oops. For eight. We can draw point here. Yeah, the blues working. Okay. Drop point here and then make a small tangent line. And then for 16 which is way out here, we'll draw this tangent line on notice that this is a lot steeper than this line. So we know that the rate of decline is greater. At T equals staying. Um, and then now we're going to estimate the rate of change of end of tea on day 12. So when we estimate the rate of change on a particular day, essentially what we're doing is calculating the slope of the secret line over given Interval. So we're estimating the instantaneous rate of change on day 12. So the interval that I'm going to choose for this problem is going to be a 10 and 14. The reason why I chose 14 is because we already calculated that, um, coordinate, which is right here and now. All I'm going to do is I'm going to calculate the coordinates for 10. So when I plug in 10 back into the function, my wife corner is going to be 11.364 And now, when I plugged this back into the rate of change equation, I get 7.2 for nine oneness, 11.364 all over, uh, 14 minus 10. And my answer is going to be 1.29 Make sure you put that negative over here because we're subtracting a number greater than seven on the top, so negative 1.29 percent each day. So, in sum, all we're doing in this problem is looking at seek it lines and using this change of whatever changes, a formula to calculate average rate of change. And we're also looking at a tangent lines in order to help us compare rates of declining given points. And when we're estimating instantaneous ray of change. What we want to do is essentially calculate the slope of a secret line, using the formula that we mentioned on the very beginning of this problem, which is this change of while retreating six.