Respuesta :
Answer:
(a) Bacterial 1 had a faster rate of growth.
(b) The population of f(x) always exceed the population of g(x). In other words, population of g(x) cannot exceed the population of f(x).
Step-by-step explanation:
Consider the given functions are
[tex]f(x)=2x^2+7[/tex]
[tex]g(x)=2x[/tex]
where, x is the time (in hours) and f(x) and g(x) are the number of bacteria (in thousands).
(a)
The rate of change of a function f(x) on [a,b] is
[tex]m=\frac{f(b)-f(a)}{b-a}[/tex]
Rate of change between third and sixth hour of first function is
[tex]m_1=\frac{f(6)-f(3)}{6-3}[/tex]
[tex]m_1=\frac{(2(6)^2+7)-(2(3)^2+7)}{6-3}[/tex]
[tex]m_1=\frac{79-25}{3}[/tex]
[tex]m_1=\frac{54}{3}[/tex]
[tex]m_1=18[/tex]
Rate of change between third and sixth hour of second function is
[tex]m_2=\frac{g(6)-g(3)}{6-3}[/tex]
[tex]m_2=\frac{2(6)-2(3)}{6-3}[/tex]
[tex]m_2=\frac{12-6}{3}[/tex]
[tex]m_2=\frac{6}{3}[/tex]
[tex]m_2=2[/tex]
Since [tex]m_1>m_2[/tex], therefore bacterial 1 had a faster rate of growth.
(b)
The initial population of f(x) is 7 and it increases exponentially.
The initial population of g(x) is 0 and it increases linearly.
It means population of f(x) always exceed the population of g(x).
In other words, population of g(x) cannot exceed the population of f(x).
