Question

Help please. High temperatures for several days are shown in the table. Which answer describes the average rate of change from day 3 to day 5 ?

Answer 1

-3

Explanation:

Average rate of a function f(x) in the interval a to b is given by

Average rate of change =

`(f(b)-f(a))/(b-a)`

Here end points are given as 3 and 5

a=3 and b=5

b-a = 2

From the table we can find out values of f(3) and f(5)

`f(3) =59\\f(5) =53\\f(5)-f(3) =-6`

Average rate of change = -6/2=-3

Negative sign indicates change is decrease.

I.e. for 1 unit change in x, on an average 3 units of f decreases.

Answer 2

The high temperature changed by an average of -3 degrees per day from day 3 to day 5.

Explanation:

We are given a table which holds the record of highest temperatures recorded in 5 days.

We are to determine whether which of the given answer options describes the average rate of change from day 3 to day 5.

Avg. rate of change from day 3 to 5 =
`(59-53)/(2) =3`

Therefore, the correct answer option is:

The high temperature changed by an average of -3 degrees per day from day 3 to day 5.

(here negative sign shows the decrease in the temperature)