Question

People are entering a building at a rate modeled by f (t) people per hour and exiting the building at a rate modeled by g (t) people per hour, where t is measured in hours. The functions f and g are nonnegative and differentiable for all times t. Which of the following inequalities indicates that the rate of change of the number of people in the building is increasing at time t? o f (t) > 0 f (t)-9(t) > 0 o f (t)>0 of'(t)-g'(t) > 0

Answer 1

Answer:

The correct option is D) $f'(t)-g'(t) > 0$

Step-by-step explanation:

Consider the provided information.

People are entering a building at a rate modeled by f (t) people per hour and exiting the building at a rate modeled by g (t) people per hour,

The change of number of people in building is:

$h(x)=f(t)-g(t)$

Where f(t) is people entering in building and g(t) is exiting from the building.

It is given that "The functions f and g are non negative and differentiable for all times t."

We need to find the the rate of change of the number of people in the building.

Differentiate the above function with respect to time:

$h'(x)=\frac{d}{dt}[f(t)-g(t)]$

$h'(x)=f'(t)-g'(t)$

It is given that the rate of change of the number of people in the building is increasing at time t.

That means $h'(x)>0$

Therefore, $f'(t)-g'(t)>0$

Hence, the correct option is D) $f'(t)-g'(t) > 0$