The birth rate, B, in births per hour, of a bacteria population is given in the figure. The curve marked D gives the death rate, in deaths per hour, of the same population. (a) Explain what the shape of each of these graphs tells you about the population. bacteria/hour B D 10 15 20 time (hours) In the beginning the birth and death rates are both increasing. Which is growing faster? The death rate is growing faster. Later, the birth rate decreases. After about 11 hours, the population begins increasing. (b) Use the graphs to find the time at which the net rate of increase of the population is at a maximum. The net rate of increase is at a maximum after about 12 hours.

The birth rate, B, in births per hour, of a bacteria population is given in the figure. The curve marked D gives the death rate, in deaths per hour, of the same population. (a) Explain what the shape of each of these graphs tells you about the population. bacteria/hour B D 10 15 20 time (hours) In the beginning the birth and death rates are both increasing. Which is growing faster? The death rate is growing faster. Later, the birth rate decreases. After about 11 hours, the population begins increasing. (b) Use the graphs to find the time at which the net rate of increase of the population is at a maximum. The net rate of increase is at a maximum after about 12 hours.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

The birth rate, B, in births per hour, of a
bacteria/hour
bacteria population is given in the figure.
The curve marked D gives the death rate,
in deaths per hour, of the same population.
B
D
(a) Explain what the shape of each of these
graphs tells you about the population.
10
15
20
time (hours)
In the beginning the birth and death rates are both increasing.
Which is growing faster? The death rate is growing faster.
Later, the birth rate
decreases.
After about 11 hours, the population begins increasing.
(b) Use the graphs to find the time at which the net rate of increase
of the population is at a maximum.
The net rate of increase
is at a maximum after about
12 hours.

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