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Suppose that W = f (t) represents the weight of a particular baby calf t = days after it is born: Interpret the meaning of the following statements:f(4)=96f'(4...

Question

Suppose that W = f (t) represents the weight of a particular baby calf t = days after it is born: Interpret the meaning of the following statements:f(4)=96f'(4)=2.5

Suppose that W = f (t) represents the weight of a particular baby calf t = days after it is born: Interpret the meaning of the following statements: f(4)=96 f'(4)=2.5



Answers

The weight, $w,$ in kilograms, of a baby is a function $f(t)$ of her age, $t$, in months. (a) What does $f(2.5)=5.67$ tell you? (b) What does $f^{\prime}(2.5) / f(2.5)=0.13$ tell you?

If W. Of T represents the weight of a puppy in Pounds T weeks after it is born, then the interpretation of W prime of 15 equaling 1.75 would represent the following 15 weeks after the puppy is born. The weight of the puppy is increasing by £1.75 each week, increasing because the derivative is positive and recall that when the derivative is positive but the function is increasing.

So wait w zero adverse. We are God when he calls to zero Wait, he calls to w zero and the differential function. We have the w over the T eco's to 10 1200 minus w. And now we separate variables will have won over 1200 minus W d w equals to the key. So we integrate both sides. We all have long one salt 1200 minus w equals thio t plus a constant So 1002 100 mine sw equals to eat power of t times the constant let's say those constant obviously equals to see So when he goes to the role will have 1000 my nose, Uh, at at the time he equals zero w equals to w zero so it goes to see as a result, will have won 103,200 miners W e cosa E T. Times 1200 miners w zero

All right. So this question is asking us to create a um an equation that calculates the rate of change between week 33 and week 39. So if we go to week 33 in our chart, we can see that the weight is going to be 67 .68. And if we go to week 39, we see that the weight is going to be 1.16.00. So we can use this bits of information. Think of it like X and Y. Right. And whenever we are calculating rate of change, we use the formula um X two or I'm sorry, Y tu minus Y one divided by X two minus X one. This gives us our rate. Alright, If we're thinking of terms of Y equals mx plus B. This M is our rate or are slip If you're thinking in terms of a graph. So whenever you plug in this, Y two minus Y one divided by X two minus x one you're calculating? Um So we can go ahead and plug in our points. All right. So we're starting off with Y two. Right, Which is 1 16 minus Y one which is 67.68 You divided by X two which is 39 and subtracted by X one which is 33 1 16 minus one minus 67.68 is going to give you 48.32 and 39 minus 33 is six. Whenever you divide that you get 8.1. So this is going to be our rate. Now if you look at your answer choices, the only answer choice that has a rate of 8.1 is answer choice c. So honestly you could just circle c and move on. But if you wanted to finish writing out the equation, we can totally do that. So right now we have um if we were thinking of terms and Y equals mx plus B, we still have to solve for R. B. But we do have points we can use from our graph so I could plug in Y equals mx plus B. I could say my wife is 67.68 I know my rate is 8.1. My ex in this case is going to be 33 and I'm solving for B. Right, we could do 8.1 times 33 and get to 67.3 Saturday equal to 67.68. And again we urge is solving for B. If we keep on going we would just add or subtract both sides by um 267.3. And whenever we do that we have b equals about 200 or negative 200. Sorry about that. So you're subtracting negative 267.3 on both sides and that will give you about three. That'll give you about negative 200. So that's what you finish writing your equation as right. We set our M was 8.1 RB as negative 200. So whenever you write that out you have W equals 8.1 Times T -200. So this is going to be your final answer, which is cancer choice c.

Okay, So for that column, Number eight were asked to find how, when the milk consumption of a newborn cow is greatest and how much it is. So we're given this formula to try to figure it out. It's a function p of X equals negative 0.2 x squared plus 1.3 x plus 6.2. All right, so there's a few steps we can take in the beginning to set up the problem and approach solving it. So the 1st 1 we know that p of x, we consent p of X equals wide suggest to substitute it to make make the equation much more familiar to us. So using X and why we get why equals negative 0.2 x squared plus 1.3 x plus six points use essentially the same thing. But the only thing we're doing, the only thing we're changing is subsiding. Why, for p of X and then the second thing is that we realize this is a quadratic formula because we have the X squared over here, and because of that, we want to figure out if it's up or down. So is that isn't an open facing parabola and that it would look something like this open facing, so facing towards the top, Or does it look something a little bit more like this? The problem is facing down. So we, as we see here, this one has a maximum by value. Versus this one has a minimum value. So we can see this by looking at its the, um, the coefficient over here. So we can you we can rewrite the standard formula for a problem as why equals a X squared plus B x plus c and then So the way that we find out if it's up or down, we, if a is greater than zero, that it must be an upward facing for Ebola. However, if a is less than zero, in which case this is because it's a negative number. Negative 0.2. It must be a downward facing for Ebola. So we see here half speed, downward facing problem. So it must look something a little bit more like this. Not exactly, but rough sketch um, and then the next step is to find to use the vertex for a minute to find X so we can use his formula negative. Be over to a Essentially we get We use the same music coefficients A, B and C But using these ones in this formula, we get B is 1.3 over two times negative 0.2 and then using a calculator, we get that this is 3.25 So this is the ex Formula X co ordinate so equals X. And the next thing we want to find out, we want to find why So X is the number of weeks old. So that is, that answers the question of wind. The mill conceptions greatest. That is, in 3.25 weeks. So 3.25 weeks. So that answers the first part of the question. However, we still want to know how much does that? Um, how much milk doesn't consume. So for that, we want to find out why. So then the next Abbasi use acts, define the y, value the vortex on. We do that by simply substituting. So we get why equals you get a 0.2 3.25 squared plus 1.3 x plus 6.2 and we just use a calculator, and then eventually we find the answer, which is eight 0.31 to 5 about so that is the amount of milk consumed.


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