Vraag 10

In de rest van deze opgave gaan we uit van een ander prooi-roofdiermodel:

\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\frac14\pi\left(t+1\right)\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\frac14\pi\left(t+1\right)\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\frac14\pi\left(t+1\right)\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\frac14\pi\left(t+\right)\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\frac14\pi\left(t\right)\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\frac14\pi\left(\right)\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\frac14\pi\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\frac14\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\frac14\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\frac14\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\frac14\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\left(\right)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\cos\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\cdot\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1300\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+130\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+13\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+1\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500+\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2500\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=250\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=25\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=2\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^{}\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+x\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+x-\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+x-2\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+x-2)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+x-2)(\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+x-2)(x\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+x-2)(x-\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+x-2)(x-3\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-3\right)\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t-\right)\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(t\right)\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\left(\right)\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\pi\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\frac14\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\left(\right)\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\sin\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\cdot\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3400\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+340\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+34\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+3\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800+\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4800\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=480\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=48\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=4\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^{}\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^{}\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^2\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^2-\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^2-7\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^2-7x\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^2-7x-\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^2-7x-2\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^2-7x-29\\ & r(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^2-7x-29\\ & (t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^2-7x-29\\ & g(t)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^2-7x-29\\ & g()=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(t)=x^3-x^2-7x-29\\ & g(x)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p()=x^3-x^2-7x-29\\ & g(x)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & p(x)=x^3-x^2-7x-29\\ & g(x)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & (x)=x^3-x^2-7x-29\\ & g(x)=(x^2+x-2)(x-3)\end{aligned}\begin{aligned} & f(x)=x^{3}-x^{2}-7 x-29 \\ & g(x)=(x^{2}+x-2)(x-3) \end{aligned}

Hierin is$phet aantal prooidieren,$rhet aantal roofdieren en$tde tijd in jaren. In figuur 2 zijn de grafieken van$pen$rgeschetst.

In elke periode is er één moment waarop de groeisnelheid van het aantal prooidieren maximaal is. In het bijbehorende punt op de grafiek is de helling dus maximaal.