Question

the system of the population of a culture of tumor cells is given by p(t)=\frac{3200t}{t + 1}. find and interpret lim_{t
ightarrowinfty}p(t). select the correct choice below, and fill in the answer box if necessary. a. lim_{t
ightarrowinfty}p(t)=3200 b. the limit does not exist and is neither -infty nor infty. choose the correct statement. a. a steady - state for the given system is the value of lim_{t
ightarrowinfty}p(t). b. a steady - state for the given system does not exist.

Explanation:

Step1: Divide numerator and denominator by t

We have $p(t)=\frac{3200t}{t + 1}$. Dividing both numerator and denominator by $t$ gives $\lim_{t
ightarrow\infty}\frac{3200t/t}{t/t+1/t}=\lim_{t
ightarrow\infty}\frac{3200}{1 + 1/t}$.

Step2: Evaluate the limit

As $t
ightarrow\infty$, $\frac{1}{t}
ightarrow0$. So $\lim_{t
ightarrow\infty}\frac{3200}{1 + 1/t}=\frac{3200}{1+0}=3200$.

For the second - part, a steady - state of a system is often defined as the value of the limit as time (in this case $t$) goes to infinity. Since $\lim_{t
ightarrow\infty}p(t) = 3200$, a steady state for the given system is the value of $\lim_{t
ightarrow\infty}p(t)$.

Answer:

A. $\lim_{t
ightarrow\infty}p(t)=3200$
A. A steady state for the given system is the value of $\lim_{t
ightarrow\infty}p(t)$