3300tThe population of a culture of tumor cells is given by p (t)where t is the time in months.t+3a. Find lim,op(t). b. Interpret your answer.

Answered: a. Find lim00 P (t). b. Interpret your…

Math

Calculus

a. Find lim00 P (t). b. Interpret your answer.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.6: Rational Functions

Problem 2E

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Concept explainers

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

3300t
The population of a culture of tumor cells is given by p (t)
where t is the time in months.
t+3
a. Find lim,op(t). b. Interpret your answer.

Expert Solution

Step 1

Given that :

The population of a culture of tumor cells is given by p(t) = $\frac{3300 t}{t + 3}$ , where t is the time in months.

Step 2

a) To find $\lim_{t \to \infty} p (t)$ :

$\lim_{t \to \infty} p (t) = \lim_{t \to \infty} \frac{3300 t}{t + 3} = \lim_{t \to \infty} \frac{t (3300)}{t (1 + \frac{3}{t})} = \lim_{t \to \infty} \frac{3300}{(1 + \frac{3}{t})} = \frac{3300}{1 + 0} = 3300 \Rightarrow \lim_{t \to \infty} p (t) = 3300$

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