Q24. - Algebra 1

Question

The graph shows the population growth in Leesburg, Florida, since 2000.

1. For which time period is the rate of change the greatest? 
2. Explain the meaning of the slope from 2000 to 2006.

Step-by-Step Solution

Answer

1. The required time period is represented by 2003-2004.
2. The required slope is represented by 0.79 and it is representing the increment in the growth. 

Part a. Step 1. Determine the method which can be used to determine the time period.

Spot the interval on the graph which has the longest gap between the points. 

Part a. Step 2. Determine the required interval.

The interval 2003-2004 is the interval which shows that longest gap between the points.

Part a. Step 3. Write the conclusion.

The obtained interval 2003-2004 represents the longest gap between the points so it is the required interval.

Part b. Step 1. Determine the points required to get the slope.

Take the help of provided graph and write the points associated with the provided years.

$\left(2000,15\right)\left(2006,19.75\right)$ 

Part b. Step 2. Determine the required slope.

Take the help of formula for slope of a line represented by $m=\frac{y_2-y_1}{x_2-x_1}$ in which the required values can be filled by using the obtained points as they are in the form of $\left(x_1,y_1\right) \left(x_2,y_2\right)$.

 $\begin{array}{c}m=\frac{19.75-15}{2006-2000}\\ =\frac{4.75}{6}\\ =0.79\end{array}$

Part b. Step 3. Write the meaning.

The obtained slope represents the increment in the growth.