Q14. - Algebra 2

Question

For Exercises 12-14, use the table that shows the temperatures at different times on March 23, 2002.

During what 2-hour period was the average rate of change of the temperature the least?

Step-by-Step Solution

Answer

The time interval $2:00\text{ P.M.}-4:00\text{ P.M.}$  2-hour period has the minimum average rate of change of the temperature is least.

Step 1- Given information

Table of the data,

Step 2- Formula used

The slope formula (rate of change) m of a line is:

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

Where, m is slope of the line which is passes through the points $(x_1,y_1),(x_2,y_2)\text{ and }{x}_1\ne x_2.$

Step 3- To find the Rate of change

According to the given data table,

Temperature change at the time interval is:

 $8:00A.M.-10:00A.M.$ is 11 and average rate change of temperature is $5.5.$ $2:00\text{ P.M.}-4:00\text{ P.M.}$

$10:00\text{ A.M.}-12:00\text{ P.M.}$ is 8 and average rate change of temperature is $4$.

$12:00\text{ P.M.}-2:00\text{ P.M.}$is 8 and average rate change of temperature is $4$.

$2:00\text{ P.M.}-4:00\text{ P.M.}$ is 2 and average rate change of temperature is $1$.

Hence, the time interval $2:00\text{ P.M.}-4:00\text{ P.M.}$  2-hour period has the minimum average rate of change of the temperature is least.