(Solved): A typical population curve is shown in the figure. The population is small at t=0 and increases tow ...

A typical population curve is shown in the figure. The population is small at $\mathrm{t}=0$ and increases toward a steady-state level called the carrying capacity. The population of a species is given by the function $P(t)=\frac{K{t}^2}{t^2+b}$, where $t?0$ is measured in years and $K$ and $b$ are positive real numbers. Complete parts (a) through (c) below. a. With $K=500$ and $b=42$, what is $\lim P(t)$, the carrying capacity of the population? ${\lim }_{t??}P(t)=500\text{ (Simplify your answer.) }$ b. With $\mathrm{K}=500$ and $\mathrm{b}=42$, when does the maximum growth rate occur? The maximum growth rate occurs at $\mathrm{t}=$ (Type an exact answer, using radicals as needed.)