Question

The number of crimes that occurred in a certain city per 1000 people had decreased from 46.1 in 1920 to 45.3 in 1940. Find the average rate of change in the number of crimes per 1000 people that occurred from 1920 to 1940.

Answer 1

-0.04 = decrease of 4%

Explanation:

`\boxed{\begin{minipage}{6.3 cm}\underline{Average rate of change of function $f(x)$}\\\\$(f(b)-f(a))/(b-a)$\\\\over the interval $a \leq x \leq b$\\\end{minipage}}`

Given interval:

• 1920 ≤ x ≤ 1940

Therefore:

• a = 1920
• b = 1940

Given values:

• f(a) = f(1920) = 46.1
• f(b) = f(1940) = 45.3

Substitute the values into the formula:

`\begin{aligned}\textsf{Average rate of change}&=(f(1940)-f(1920))/(1940-1920)\\\\&=(45.3-46.1)/(1940-1920)\\\\&=(-0.8)/(20)\\\\&=-0.04\end{aligned}`

Therefore, the average rate of change was -0.04 which is a decrease of 4%.