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\to\infty}p(t). select the correct choice below, and fill in the answer box if necessary. a. \lim_{t\to\infty}p(t)= b. the limit does not exist and is neither -\infty nor \infty.

Explanation:

Step1: Divide numerator and denominator by t

Divide both the numerator and denominator of $p(t)=\frac{3200t}{t + 1}$ by $t$. We get $\lim_{t
ightarrow\infty}\frac{3200t/t}{(t + 1)/t}=\lim_{t
ightarrow\infty}\frac{3200}{1+\frac{1}{t}}$.

Step2: Evaluate the limit

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

Step3: Calculate the result

$\frac{3200}{1+0}=3200$.

Answer:

A. $\lim_{t
ightarrow\infty}p(t)=3200$