Renee is trying to determine the optimal cooking method for their turkey using different cooking temperatures 375*C(+1 and 3259C(-1)), and wrapping in tinfoil (with...

Biologieal Researeh Stephanie, a biologist who does research for the poultry industry, models the population $P$ of wild turkeys, $t$ days after being left to reproduce, with the function
$$
P(t)=-0.00001 t^{3}+0.002 t^{2}+1.5 t+100
$$
(a) Graph the function $y=P(t)$ for appropriate values of $t$
(b) Find what the maximum turkey population is and when it occurs.
(e) Assuming that this model continues to be accurate, when will this turkey population become extinct?
(d) Writing to Learn Create a scenario that could explain the growth exhibited by this turkey population.

Okay, 3.4. So section 3 to 4 and we're looking at problem number 59. Photograph. It looks sort of like this with oven temperatures. Ah, so we're starting out in degrees, so we got degrees. Looks like Fahrenheit. So at zero degrees, 100 200 300 405 100. And then we got time of day starting at 8 30 So at eight. 30 and then at 9 30 10 30 11 30 and 12 30. So find the So here's our temperatures T So temperature is T, whereas to find the derivative at 0.5, So time is after 8 30 So to find the derivative at 0.5 would mean what's the derivative at that point? That's part a. Then we're asked to find the derivative at three. At three hours is gonna be at 11. 30 and then at four hours, that's the derivative at 12. 30. So the derivative is the rate of change is so this is gonna be approximate year. So if I were to draw the slope of a line that is changing to the curve at that point, okay, so sort of hard with the accuracy of this graph. But if I see something like that, it looks like, you know, it looks like to get to about halfway Mark. So what is the difference in why, over a difference in X so far to make a triangle Delta y Delta X. So, in this case, um, don't go quite there. So it's a little bit approximately 2 50 Um, So I'm getting somewhere about, um, you know, somewhere between two and 200 202 50 somewhere. And there is that temperature change. But the delta y Sorry, this is a Delta X here. So the change in X from about here to hears about one hour. So it looks like this derivative here. So t prime at 1/2 of an hour, it's gonna be somewhere about, you know, maybe 220. Okay, so somewhere in this is approximate. So if I look at what happens at 11. 30 if I had a tangent line here, Okay, so it looks like in this case Ah, not a great tension line, but, um, so somewhere right in here. So to go from here to here, this Delta X is gonna be one. And it looks like the change in temperature here is gonna be one. So it looks like about, um so would say it looks like about 100 and 50 maybe degrees so somewhere. Um, if I look at that, um I mean, try that one more time. Let me re draw that. Change that line. Just seem a little bit more accurate there. So if I look at this once more, um so if I draw a change, that line at this point, Sorry about that. Um, so me redraw the curve there real quick. The curve is doing something like this if I redraw that tangent line at 11. 30. So somewhere up here, so it looks like I see a difference of about looking at 1 50 So it's somewhere around the negative slope, so maybe around the negative, you know, 1 50 to 200 um, would be the slope that I would be seeing there. Okay. And then if I look at four tangent line here, Slope is gonna be about zero. So when I look at T prime at three. Um, so that's somewhere in the negative range. Maybe, you know, negative 1 52 negative 200. Approximate and then T prime at four is going to be zero. So it tells me that when a positive So the big thing is this is positive. My oven is warming. The temperatures are increasing over here. T prime is a negative number. My oven is cooling, Temperatures are going down right here. I've got a steady state. My temperatures were remaining about the same and they're saying, When did this turkey get put in the oven? Will you put the turkey in the oven, which is cold? The temperature's gonna drop. It looks like that happened somewhere about right here, so that looks like about 11. 15 would correspond to when that turkey was put in.

Hello everyone. I will be going through my enumerated interview question. I have taken a screenshot of the question in the book and I put it here in my note pad. I'll be reading the question 1st, going through some of the important points and then I will be going through my answer. So roast Turkey is taken from an oven when its temperature has reached 185°F so that is right there on the graph. Um that's 85°F And that's at time zero And it's placed on a table in a room where the room temperature is 75°F so we're gonna see that green line, that's the room temperature. And the graph shows how the temperature of the turkey decreases and eventually approaches the room temperature. So as we can see it just approaching that green line um and the temperature of turkey slowly becoming room temperature. Uh Now we by measuring the slope of the tangent, estimate the rate of change of the temperature after an hour. So it's very important to note that it's as measure not calculate. So we will be measuring the slope of the tangent After an hour. So often hours after 60 minutes, which is right there on the X axis which is representing time in this case. So we want the slope of the tangent right there at that point p in the graph. So to do that we will take two points X one Y 1 and X two Y 2. The first one. I will pick time will be 25 minutes approximately And 150 550. Fahrenheit, that's the temperature at 25 minutes. And at 95 minutes, the temperature appears to be 100° during high. So we will take those two points and do rise over run to get the slope. So rise over. Run is the same as Taking the two x 1 y one until I'm just rewriting here for clarity As 25 and one 50 And then 95 and 100. So rise over run. We will do. Why two minus why? One Over X 2 -11. Now we plug in our numbers, We get 1 to 100 -150 and 95 minus 25. So that gives us -50/70, Which is -5/7. So we can say approximately the slope of the tangent at the point P, which is 60 minutes to equal 60. So approximately the slope of the tangent line, ah 60 minutes is minus five sevens. So that's the slope. But we can also say uh approximately the rate of change is uh minus 57 degrees Fahrenheit permanent. Right? So because it's a rate of change, we include the unit here and we want our quantity in this case the temperature to be changing over a certain period of time. So After an hour, the rate of change is -5 over seven F per minute, which is approximately -7 fan high per minute. So you can say or you're speaking after an hour, you can say approximately, the turkey is cooling down .7°F permanent. Right? Because it's cooling down the temperatures negatives, the rate of teens has negative temperatures, so it's cooling down. Thank you. And I hope you enjoyed that explanation.

Hello everyone. I will be going through my enumerated interview question. I have taken a screenshot of the question in the book and I put it here in my note pad. I'll be reading the question 1st, going through some of the important points and then I will be going through my answer. So roast Turkey is taken from an oven when its temperature has reached 185°F so that is right there on the graph. Um that's 85°F And that's at time zero And it's placed on a table in a room where the room temperature is 75°F so we're gonna see that green line, that's the room temperature. And the graph shows how the temperature of the turkey decreases and eventually approaches the room temperature. So as we can see it just approaching that green line um and the temperature of turkey slowly becoming room temperature. Uh Now we by measuring the slope of the tangent, estimate the rate of change of the temperature after an hour. So it's very important to note that it's as measure not calculate. So we will be measuring the slope of the tangent After an hour. So often hours after 60 minutes, which is right there on the X axis which is representing time in this case. So we want the slope of the tangent right there at that point p in the graph. So to do that we will take two points X one Y 1 and X two Y 2. The first one. I will pick time will be 25 minutes approximately And 150 550. Fahrenheit, that's the temperature at 25 minutes. And at 95 minutes, the temperature appears to be 100° during high. So we will take those two points and do rise over run to get the slope. So rise over. Run is the same as Taking the two x 1 y one until I'm just rewriting here for clarity As 25 and one 50 And then 95 and 100. So rise over run. We will do. Why two minus why? One Over X 2 -11. Now we plug in our numbers, We get 1 to 100 -150 and 95 minus 25. So that gives us -50/70, Which is -5/7. So we can say approximately the slope of the tangent at the point P, which is 60 minutes to equal 60. So approximately the slope of the tangent line, ah 60 minutes is minus five sevens. So that's the slope. But we can also say uh approximately the rate of change is uh minus 57 degrees Fahrenheit permanent. Right? So because it's a rate of change, we include the unit here and we want our quantity in this case the temperature to be changing over a certain period of time. So After an hour, the rate of change is -5 over seven F per minute, which is approximately -7 fan high per minute. So you can say or you're speaking after an hour, you can say approximately, the turkey is cooling down .7°F permanent. Right? Because it's cooling down the temperatures negatives, the rate of teens has negative temperatures, so it's cooling down. Thank you. And I hope you enjoyed that explanation.