Concept explainers
Growth of Bacteria The number of bacteria present in a culture at time (in hours) obeys the model .
(a) Determine the number of bacteria at hours.
(b) What is the growth rate of the bacteria?
(c) Graph the function using a graphing utility.
(d) What is the population after 4 hours?
(e) When will the number of bacteria reach 1700?
(f) When will the number of bacteria double?
To find:
a. Determine the number of bacteria at hours.
Answer to Problem 2AYU
Solution:
a. 1000
Explanation of Solution
Given:
Calculation:
Let us consider 1000 bacteria initially and the number of bacteria after hours will be
a. Let us consider the initial state. Then
To find:
b. What is the growth rate of the bacteria?
Answer to Problem 2AYU
Solution:
b.
Explanation of Solution
Given:
Calculation:
Let us consider 1000 bacteria initially and the number of bacteria after hours will be
b. Let us compare the above model with where defines the growth rate of the model. Then .
To find:
c. Graph the function using a graphing utility.
Answer to Problem 2AYU
Solution:
c.
Explanation of Solution
Given:
Calculation:
Let us consider 1000 bacteria initially and the number of bacteria after hours will be
c. Graph:
To find:
d. What is the population after 4 hours?
Answer to Problem 2AYU
Solution:
d. 1041
Explanation of Solution
Given:
Calculation:
Let us consider 1000 bacteria initially and the number of bacteria after hours will be
d. Let us consider hours. Then
To find:
e. When will the number of bacteria reach 1700?
Answer to Problem 2AYU
Solution:
e.
Explanation of Solution
Given:
Calculation:
Let us consider 1000 bacteria initially and the number of bacteria after hours will be
e. Let us consider . Then
Taking log on both sides we get,
hours
To find:
f. When will the number of bacteria double?
Answer to Problem 2AYU
Solution:
f.
Explanation of Solution
Given:
Calculation:
Let us consider 1000 bacteria initially and the number of bacteria after hours will be
f. Let us consider .
Taking log on both sides we get,
hours
Chapter 5 Solutions
Precalculus
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