3.The snow starts at a depth of 10 inches and melts to 2 inches over the span of 4 hours. Determine the rate of change over the interval 0≤x≤4
A.4 inches per hour
B.2 inches per hour
C.8 inches per hour
D.12 inch per hour
4.The population in a neighborhood increased from 120 to 156 people from 1990 to 1994. Find the rate of change over the interval 1990≤x≤1994.
A.1/9 of a person per year
B.9 people per year
C.36 people per year
D.4 people per year
5.The temperature increases from 60 degrees Fahrenheit to 84 degrees Fahrenheit from 8 in the morning to 12 in the afternoon. Find the rate of change over the interval 8≤x≤12
A.16 of a degree Fahrenheit per hour
B.4 degrees Fahrenheit per hour
C.6 degrees Fahrenheit per hour
D.24 degrees Fahrenheit per hour
What are your choices?
Huh?
What are your answer choices. We are not giving you the answers we are just checking them.
To determine the rate of change over a given interval, we need to find the average rate of change by dividing the change in the dependent variable by the change in the independent variable.
For question 3:
We start with a snow depth of 10 inches and it decreases to 2 inches over 4 hours. The change in depth is 10 inches - 2 inches = 8 inches. The change in time is 4 hours - 0 hours = 4 hours.
To find the average rate of change, we divide the change in depth (8 inches) by the change in time (4 hours):
Average rate of change = 8 inches / 4 hours = 2 inches per hour.
Therefore, the answer is B. 2 inches per hour.
For question 4:
The population increases from 120 people to 156 people over a span of 4 years. The change in population is 156 people - 120 people = 36 people. The change in time is 1994 - 1990 = 4 years.
To find the average rate of change, we divide the change in population (36 people) by the change in time (4 years):
Average rate of change = 36 people / 4 years = 9 people per year.
Therefore, the answer is B. 9 people per year.
For question 5:
The temperature increases from 60 degrees Fahrenheit to 84 degrees Fahrenheit over a span of 4 hours. The change in temperature is 84 degrees Fahrenheit - 60 degrees Fahrenheit = 24 degrees Fahrenheit. The change in time is 12 hours - 8 hours = 4 hours.
To find the average rate of change, we divide the change in temperature (24 degrees Fahrenheit) by the change in time (4 hours):
Average rate of change = 24 degrees Fahrenheit / 4 hours = 6 degrees Fahrenheit per hour.
Therefore, the answer is C. 6 degrees Fahrenheit per hour.