The answer & explanation for this question is given in the attachment below.
Answer:
Dreistein: The world will continue to warm, but there will be no end of the world. But eventually it will get too hot for everyone.
Step-by-step explanation:
The first step to solve this question is solving the differential equation.
[tex]\frac{dy}{dt} = \sqrt{y}[/tex]
We use the variable separation method
[tex]\frac{dy}{\sqrt{y}} = dt[/tex]
[tex]y^{-0.5} dy = dt[/tex]
Integrating both sides
[tex]\frac{y^{-0.5 + 1}}{-0.5 + 1} = t + K[/tex]
K is the constant of integration
[tex]2y^{0.5} = t + K[/tex]
[tex]2\sqrt{y} = t + K[/tex]
[tex]\sqrt{y} = \frac{t + K}{2}[/tex]
[tex](\sqrt{y})^{2} = (\frac{t+K}{2})^{2}[/tex]
[tex]y = \frac{(t + K)^{2}}{4}[/tex]
y(0) = 1.
We use this to find K. So
[tex]1 = \frac{(0 + K)^{2}}{4}[/tex]
[tex]K^{2} = 4[/tex]
[tex]K = \pm 2[/tex]
So
[tex]y = \frac{(t \pm 2)^{2}}{4}[/tex]
Quadratic equation, with positive concavity, that is, an increasing function.
A quadratic equation has no equilibrium point.
However, while the temperature will increase, it will not become infinite in a finite time.
So the correct answer is:
Dreistein: The world will continue to warm, but there will be no end of the world. But eventually it will get too hot for everyone.
