# 5.1.313 AP Calculus Exam DE on bird weight

• MHB
• karush
In summary, the graph suggests that there is a decrease in weight as the bird's listening frequency decreases.
karush
Gold Member
MHB
View attachment 9342
I just posted a image due to overleaf newcommands and graph

ok (a) if we use f(20) then the $B=0$ so their no weight gain.

(b), (c), was a little baffled and not sure how this graph was derived...

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(a) $\dfrac{dB}{dt} > 0$ for $20 \le B < 100$ ... what does that say about the change in the bird's weight?

(b) $\dfrac{d}{dt} \left[\dfrac{dB}{dt} = \dfrac{1}{5}(100-B) \right]$

$\dfrac{d^2B}{dt^2} = -\dfrac{1}{5}(100-B) < 0 \implies B(t) \text{ is concave down everywhere}$

(c) $\dfrac{-1}{100-B} \, dt = -\dfrac{1}{5} \, dt$

$\log|100-B| = -\dfrac{t}{5} + C$

$B(0) = 20 \implies C = \log(80)$

$100-B = 80e^{-t/5} \implies B = 100 - 80e^{-t/5}$

the function $B(t)$ is an example of inhibited exponential growth ... note $$\displaystyle \lim_{t \to \infty} B(t) = 100$$

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did you do the graph in tikx?

great help... appreciate all the steps

karush said:
did you do the graph in tikx?

no, I've had this free graphing program for quite a while ...

skeeter said:
(a) $\dfrac{dB}{dt} > 0$ for $20 \le B < 100$ ... what does that say about the change in the bird's weight?

(b) $\dfrac{d}{dt} \left[\dfrac{dB}{dt} = \dfrac{1}{5}(100-B) \right]$
$\dfrac{d^2B}{dt^2} = -\dfrac{1}{5}(100-B) < 0 \implies B(t) \text{ is concave down everywhere}$
No, you didn't differentiate on the right side.
$\frac{d^2B}{dt^2}= \dfrac{d}{dt}[dfrac{1}{5}(100- B)= \dfrac{1}{5}(-B)=- \frac{1}{5}B$

(c) $\dfrac{-1}{100-B} \, dt = -\dfrac{1}{5} \, dt$
The left side should be $\dfrac{-1}{100- B}dB$. not "dt".

$\log|100-B| = -\dfrac{t}{5} + C$

$B(0) = 20 \implies C = \log(80)$

$100-B = 80e^{-t/5} \implies B = 100 - 80e^{-t/5}$

the function $B(t)$ is an example of inhibited exponential growth ... note $$\displaystyle \lim_{t \to \infty} B(t) = 100$$

skeeter said:
no, I've had this free graphing program for quite a while ...

looks pretty clean and basic... which is very nice..

HallsofIvy said:
No, you didn't differentiate on the right side.
$\frac{d^2B}{dt^2}= \dfrac{d}{dt}[dfrac{1}{5}(100- B)= \dfrac{1}{5}(-B)=- \frac{1}{5}B$The left side should be $\dfrac{-1}{100- B}dB$. not "dt".

yep ... it happens.

## 1. What is the purpose of the 5.1.313 AP Calculus Exam DE on bird weight?

The purpose of the 5.1.313 AP Calculus Exam DE on bird weight is to test students' understanding and application of differential equations in the context of a real-world scenario involving the weight of birds. This exam is designed to assess students' ability to solve differential equations and interpret the results in a meaningful way.

## 2. What topics are covered in the 5.1.313 AP Calculus Exam DE on bird weight?

The 5.1.313 AP Calculus Exam DE on bird weight covers topics such as differential equations, integration, rates of change, and related rates. It also requires students to have a strong understanding of calculus concepts such as derivatives, integrals, and limits.

## 3. How is the 5.1.313 AP Calculus Exam DE on bird weight scored?

The 5.1.313 AP Calculus Exam DE on bird weight is scored on a scale of 1-5, with 5 being the highest score. The exam consists of both multiple-choice and free-response questions, and the scores are based on a combination of the two. The multiple-choice questions account for 50% of the total score, while the free-response questions make up the remaining 50%.

## 4. What skills are necessary to do well on the 5.1.313 AP Calculus Exam DE on bird weight?

To do well on the 5.1.313 AP Calculus Exam DE on bird weight, students should have a strong understanding of calculus concepts and be able to apply them to real-world scenarios. They should also have a solid understanding of differential equations and be able to solve them using various techniques. Critical thinking and problem-solving skills are also essential for success on this exam.

## 5. How can I prepare for the 5.1.313 AP Calculus Exam DE on bird weight?

To prepare for the 5.1.313 AP Calculus Exam DE on bird weight, it is important to review calculus concepts thoroughly and practice solving differential equations. It can also be helpful to work through past AP Calculus exams and practice problems to familiarize yourself with the format and types of questions that may be asked. Additionally, seeking help from a teacher or tutor can provide valuable support and guidance in preparing for this exam.

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