Question

The function graphed below represents the outside temperature (in degrees Celsius) from sunrise until 8 hours after sunrise.Over what period of time was the outside temperature decreasing? Explain.

Answer 1

The outside temperature was decreasing over the period from

t=2 hours until t=5 hours after sunrise.

Step-by-step explanation:

To determine when the outside temperature was decreasing, we examine the graph. A decreasing temperature corresponds to a negative slope on the graph. From the given graph, we observe that the temperature starts decreasing at

�

=

2

t=2 hours after sunrise and continues to decrease until

�

=

5

t=5 hours after sunrise. During this time interval, the slope of the graph is negative, indicating a downward trend in temperature.

This conclusion aligns with the fundamental concept in calculus where the slope of a function's graph represents its rate of change. A negative slope indicates a decreasing function. In the context of temperature, this implies a decline in degrees Celsius during the specified time period. The time interval from

�

=

2

t=2 to

�

=

5

t=5 hours captures the duration over which the outside temperature exhibits a consistent decreasing trend.

Understanding the behavior of a function graph provides valuable insights into the dynamics of the system it represents. In this case, recognizing the specific time interval during which the temperature is decreasing allows for a more detailed analysis of environmental conditions and can be useful for various applications, such as weather monitoring or energy management.