Question

Suppose the rate of change of rainfall, measured in inches per hour, is represented by the following function, where t is the number of hours and 0 ≤ t ≤ 8.

a. −2 in/hr
b. −2 in/hr^2
c. 9 in/hr
d. 9 in/hr^2

Answer 1

The rate of change of rainfall is -2 inches per hour.

Step-by-step explanation:

The rate of change of rainfall, measured in inches per hour, is represented by the function given. The function is:

f(t) = -2 in/hr

This means that the rate of change of rainfall is -2 inches per hour. It is important to note that the units of the rate of change are in/hr.

Answer 2

The rate of change of rainfall can be represented by a function. The correct answer is d. 9 in/hr^2.

Step-by-step explanation:

The rate of change of rainfall, measured in inches per hour, can be represented by a function. The options given are:

1. -2 in/hr
2. -2 in/hr^2
3. 9 in/hr
4. 9 in/hr^2

To determine the correct answer, we need to understand the concept of rate of change. The rate of change can be thought of as the slope of a function. In this case, the function represents the rainfall over time.

Since the rate of change is measured in inches per hour, it is the slope of the function. The correct answer can be found by determining the slope of the function at any point.

Let's look at each option:

a. -2 in/hr: This represents a constant rate of change of -2 inches per hour. It means that the rainfall is decreasing by 2 inches every hour. This is not the correct answer because the rate of change of rainfall can vary over time.

b. -2 in/hr^2: This represents a quadratic function, where the rate of change is decreasing over time. This is not the correct answer because the question asks for the rate of change of rainfall in inches per hour, not inches per hour squared.

c. 9 in/hr: This represents a constant rate of change of 9 inches per hour. It means that the rainfall is increasing by 9 inches every hour. This is not the correct answer because it does not account for any decrease in rainfall over time.

d. 9 in/hr^2: This represents a quadratic function, where the rate of change is increasing over time. This is the correct answer because it represents a changing rate of rainfall over time.