2. the functions and represent the population of two different kinds of bacteria, where x is the time (in hours) and and are the number of bacteria (in thousands).
) = 2x^2 + 7 and ) = 2x.
a. between the third and sixth hour, which bacteria had a faster rate of growth?
b. will the population of ever exceed the population of if so, at what hour?

(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

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

Rate of change between third and sixth hour of first function is

Rate of change between third and sixth hour of second function is

Since , 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).