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Growth of yeast cells In a controlled laboratory
Chapter 3, Problem 23E(choose chapter or problem)
Growth of yeast cells In a controlled laboratory experiment, yeast cells are grown in an automated cell culture system that counts the number \(P\) of cells present at hourly intervals. The number after \(t\) hours is shown in the accompanying figure.
a. Explain what is meant by the derivative \(P^{\prime}(5)\). What are its units?
b. Which is larger, \(P^{\prime}(2)\) or \(P^{\prime}(3)\)? Give a reason for your answer.
c. The quadratic curve capturing the trend of the data points (see Section 1.4) is given by \(P(t)=6.10 t^{2}-9.28 t+16.43\). Find the instantaneous rate of growth when \(t=5\) hours.
Equation Transcription:
Text Transcription:
P
t
P'(5)
P'(2)
P'(3)
P(t)=6.10t^2 - 9.28t + 16.43
t=5
Questions & Answers
QUESTION:
Growth of yeast cells In a controlled laboratory experiment, yeast cells are grown in an automated cell culture system that counts the number \(P\) of cells present at hourly intervals. The number after \(t\) hours is shown in the accompanying figure.
a. Explain what is meant by the derivative \(P^{\prime}(5)\). What are its units?
b. Which is larger, \(P^{\prime}(2)\) or \(P^{\prime}(3)\)? Give a reason for your answer.
c. The quadratic curve capturing the trend of the data points (see Section 1.4) is given by \(P(t)=6.10 t^{2}-9.28 t+16.43\). Find the instantaneous rate of growth when \(t=5\) hours.
Equation Transcription:
Text Transcription:
P
t
P'(5)
P'(2)
P'(3)
P(t)=6.10t^2 - 9.28t + 16.43
t=5
ANSWER:Solution .
Step 1 of 3.
a)
The derivative denote the rate of change of the number with respect to time at
And the unit is the no of cell per hours i.e. cell/hr