Question

in 1977, the number of high school dropouts in a country was 5217 thousand. by 2005, this number had decreased to 3120 thousand. find and interpret the average rate of change per year in the number of high school dropouts

select the correct choice below and fill in the answer boxes to complete your choice
(round to the nearest tenth as needed.)
a. the average rate of change is about \\(\square\\) thousand each year. the number of high school dropouts increased by an average of about \\(\square\\) thousand in the year 2005.
b. the average rate of change is about \\(\square\\) thousand each year. the number of high school dropouts decreased by an average of about \\(\square\\) thousand each year from 1977 to 2005.
c. the average rate of change is about \\(\square\\) thousand each year. the number of high school dropouts increased by an average of about \\(\square\\) thousand each year from 1977 to 2005.
d. the average rate of change is about \\(\square\\) thousand each year. the number of high school dropouts decreased by an average of about \\(\square\\) thousand in the year 2005.

Explanation:

Step1: Identify the formula for average rate of change

The formula for average rate of change is $\frac{\Delta y}{\Delta x}$, where $\Delta y$ is the change in the quantity (number of dropouts) and $\Delta x$ is the change in time (years).

Step2: Calculate $\Delta y$

The initial number of dropouts ($y_1$) in 1977 is 5217 thousand, and the final number ($y_2$) in 2005 is 3120 thousand. So, $\Delta y = y_2 - y_1 = 3120 - 5217 = -2097$ thousand.

Step3: Calculate $\Delta x$

The initial year ($x_1$) is 1977, and the final year ($x_2$) is 2005. So, $\Delta x = x_2 - x_1 = 2005 - 1977 = 28$ years.

Step4: Calculate the average rate of change

Using the formula, average rate of change $=\frac{\Delta y}{\Delta x}=\frac{-2097}{28}\approx -74.9$ thousand per year. The negative sign indicates a decrease.

Step5: Analyze the options

Option C says the number of high school dropouts decreased by an average of about [value] thousand each year from 1977 to 2005, which matches our calculation (negative rate means decrease over the period 1977 - 2005).

Answer:

C. The average rate of change is about -74.9 thousand each year. The number of high school dropouts decreased by an average of about 74.9 thousand each year from 1977 to 2005.