Question

the graph shows the population(in thousands) of green bay for consecutive 10 year period.
population of green bay, wisconsin
lisa claims that the average rate of change of the population from 1970 to 2000 is greater than the average rate of change for any 10 year period. is lisas claim correct? explain.
solution:
average rate of change from 1970 to 2000
=
average rate of change from 1970 to 1980
=
average rate of change from 1980 to 1990
=
average rate of change from 1990 to 2000
=
conclusion:

Explanation:

Step1: Calculate average rate of change formula

The formula for average rate of change is $\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Average rate of change from 1970 to 2000

Here, $y_1 = 156$, $y_2 = 227$, $x_1 = 1970$, $x_2 = 2000$.
$\frac{227 - 156}{2000 - 1970}=\frac{71}{30}\approx2.37$

Step3: Average rate of change from 1970 to 1980

Here, $y_1 = 156$, $y_2 = 175$, $x_1 = 1970$, $x_2 = 1980$.
$\frac{175 - 156}{1980 - 1970}=\frac{19}{10} = 1.9$

Step4: Average rate of change from 1980 to 1990

Here, $y_1 = 175$, $y_2 = 195$, $x_1 = 1980$, $x_2 = 1990$.
$\frac{195 - 175}{1990 - 1980}=\frac{20}{10}=2$

Step5: Average rate of change from 1990 to 2000

Here, $y_1 = 195$, $y_2 = 227$, $x_1 = 1990$, $x_2 = 2000$.
$\frac{227 - 195}{2000 - 1990}=\frac{32}{10} = 3.2$

Answer:

Average rate of change from 1970 to 2000: $\frac{71}{30}\approx2.37$
Average rate of change from 1970 to 1980: $1.9$
Average rate of change from 1980 to 1990: $2$
Average rate of change from 1990 to 2000: $3.2$
Lisa's claim is incorrect. Because the average rate of change from 1990 - 2000 ($3.2$) is greater than the average rate of change from 1970 - 2000 ($\approx2.37$).