Answer:
B. [tex]\frac{dP}{dt}=kt^{2}[/tex]
Explanation:
The population at time t is given by the equation P (t).
This means that P is a function of (t).
[tex]P=t^{2}[/tex]
since the rate of growth is proportional to the square of P, we have
[tex]\frac{dP}{dt}=\alpha t^{2}[/tex]
To remove the proportionality sign, we have to introduce a constant of proportionality, k.
Hence, we will have
[tex]\frac{dP}{dt}=k t^{2}[/tex]
Thus, the differential equation that describes the behavior of the function P (t) is: [tex]\frac{dP}{dt}=k t^{2}[/tex]
