Question

the temperature in Tampa increase from 4 a.m. to 4 p.m. on one day in February the table of values below represents temperature as a function of time.over which interval was the average rate of change per hour the greatest

Answer 1

The time lapse is 8 hours

To determine the average temperature you have to add the temperatures registered by the number of hours

The average rate of change is the change of value and can be calculated as

$\frac{y_2-y_1}{x_2-x_1}$

Where

(x₁, y₁)

(x₂, y₂)

are the coordinates of two points of the fucntion

Let 4pm be time zero

Between the first two points the average change of rate is

$60.1-60.1=0$

Between the second and the third

$\frac{66.9-60.1}{5-3}=3.4$

Between the third and the fourth

$\frac{75.2-66.9}{7-5}=4.15$

Between the fouth and the fifth

$\frac{78.1-75.2}{11-7}=0.725$

The greatest rate of change per hour is in the intervel 8:53a.m. to 11:53 a.m.