The data in the table show the number of bacteria in a culture at time , where is

Chapter 3, Problem 77

(choose chapter or problem)

Modeling Data The data in the table show the number N of bacteria in a culture at time t, where r is measured in days.

A model for these data is given by

\(N=\frac{24,670-35,153 t+13,250 t^{2}}{100-39 t+7 t^{2}}, \quad 1 \leq t \leq 8 \).

(a) Use a graphing utility to plot the data and graph the model.

(b) Use the model to estimate the number of bacteria when t = 10.

(c) Approximate the day when the number of bacteria is greatest.

(d) Use a computer algebra system to determine the time when the rate of increase in the number of bacteria is greatest.

(e) Find \(\lim _{t \rightarrow \infty} N(t)\).

Text Transcription:

N=24,670-35,153t+13,250t^2/100-39t+7t^2, 1 leq t leq 8

lim_t rightarrow infinity N(t)