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Bacteria Problem: Bacteria in a lab culture (Figure 7-2c) grow in such a way that the
Chapter 7, Problem 1(choose chapter or problem)
Bacteria Problem: Bacteria in a lab culture (Figure 7-2c) grow in such a way that the instantaneous rate of change of the bacteria population is directly proportional to the number of bacteria present.
a. Write a differential equation that expresses this relationship. Separate the variables and integrate the equation, solving for the number of bacteria as a function of time.
b. Suppose that initially there are 5 million bacteria. Three hours later, the number has grown to 7 million. Write the particular equation that expresses the number of millions of bacteria as a function of the number of hours. Figure 7-2c
c. Sketch the graph of bacteria versus time.
d. What will the bacteria population be one full day after the first measurement?
e. When will the population reach 1 billion (1000 million)?
Questions & Answers
QUESTION:
Bacteria Problem: Bacteria in a lab culture (Figure 7-2c) grow in such a way that the instantaneous rate of change of the bacteria population is directly proportional to the number of bacteria present.
a. Write a differential equation that expresses this relationship. Separate the variables and integrate the equation, solving for the number of bacteria as a function of time.
b. Suppose that initially there are 5 million bacteria. Three hours later, the number has grown to 7 million. Write the particular equation that expresses the number of millions of bacteria as a function of the number of hours. Figure 7-2c
c. Sketch the graph of bacteria versus time.
d. What will the bacteria population be one full day after the first measurement?
e. When will the population reach 1 billion (1000 million)?
ANSWER:Step 1 of 6
(a) Let y is the number of bacteria present and k is an arbitrary constant, then the relation can be represented as:
In variable separable form, the equation can be written as 