Owlet talons Let L (t) equal the average leng...

Question

Owlet talons Let L (t) equal the average length (in mm) of the middle talon on an Indian spotted owlet that is t weeks old, as shown in the figure.

b. Estimate the value of L'(a) for a ≥ 4 . What does this tell you about the talon lengths on these birds? (Source: ZooKeys, 132, 2011)

Accepted Answer

Below there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Given that the function H of T models the height in centimeters of a plant T days after it was planted, Estimate H of T for T is greater than or equal to 350 from the provided graph. What does this derivative indicate? Awesome. So it appears for this particular problem we're asked to solve for two separate answers. So we're asked to use our given function for H of T. And we need to note that this HFT models or function of HT will model the height in centimeters for a plant 2 days after it was planted, and our first answer that we're trying to solve for is we're trying to estimate the value of H of T for the condition that T is greater than or equal to 350 using our provided graph. And then our second answer or trying to solve first we're trying to figure out what does this derivative indicate. Awesome. So with that in mind, let's investigate our graph that is provided to us by the problem itself. And as you can see, our Y axis denotes the H of T function, and our X axis denotes T, where T is the time in days. Awesome. So with that said, we can see our curve, which is represented in red, and it appears it starts at the origin 0.00 and it steadily, very rapidly increases. And then eventually it hits a max point where it will then level out and then it will neither increase or decrease because it stabilizes. So essentially our curve starts from zero, rapidly increases, increases, increases until it reaches a point where it levels out. And stabilizes where it's neither increasing or decreasing. So it's neither increasing nor decreasing. Once it hits the stability standpoint or stability point within the leveling out of our curve. So with that said, Our first step that we need to do in order to solve this problem is we need to recall and note that the derivative of H T, so the derivative of H T, will represent the rate of change of the height of the plant with respect to time at any given day T. So once again, this will represent the rate of change, so rate of change. For once again for the height of the plant with respect to the time. At any given day, so this is for the height with respect to the time. So with that said, our next step now is we need to recall a note that there will be a tangent line that passes through the curve for T is greater than or equal to 350 and will be approximately horizontal. So as a result, this will mean that the slope of the tangent line is close to zero. So therefore, as a result, we could safely write that H of T will be approximately equal to 0 for the condition that T is greater than or equal to 350. So, as we should recall a note for this particular prompt, at 350 days, the rate of change in the plant's height will be approximately 0. So this indicates, therefore, as a result, that the plant stopped growing significantly. So, therefore, without a doubt, our final answers will have to be H of T is approximately equal to 0 for T is greater than or equal to 350. That is our first answer, and we need to note for our second answer that for 350 days after it was planted, So after it, was planted, we need to note that The plant Stopped growing, so it stopped. Growing Significantly, so it stopped growing. Significantly. Awesome. And that is our second answer. So 350 days after it was planted, Awesome. That means that our Plants stop growing significantly due to our results that we found together. So once again, to quickly recap, So our final answers has to be H T is approximately equal to 0 or T is greater than or equal to 350, and 350 days after it was planted, the plant stopped growing significantly. And that's it. That is our final answer pair. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Owlet talons Let L (t) equal the average length (in mm) of the middle talon on an Indian spotted owlet that is t weeks old, as shown in the figure.<IMAGE>
b. Estimate the value of L'(a) for a ≥ 4 . What does this tell you about the talon lengths on these birds? (Source: ZooKeys, 132, 2011)

Key Concepts

Derivative

Average Rate of Change

Biological Growth Patterns

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