Question

find the average rate of change for bicycle production from 1950 to 2000
a 0.9 million
b 1.2 million
c 1.8 million
d 2.4 million
on which interval is the average rate of change for bicycle production the greatest?
a 1950 to 1960
b 1960 to 1970
c 1970 to 1980
d 1990 to 2000

Explanation:

Step1: Find the average rate of change formula

The average rate of change formula is $\frac{f(b)-f(a)}{b - a}$. Here, $a = 1950$, $f(a)=11$ (bicycles in 1950), $b = 2000$, $f(b)=101$ (bicycles in 2000).

Step2: Substitute values into the formula

$\frac{101 - 11}{2000 - 1950}=\frac{90}{50}=1.8$

Step3: Calculate average rate of change for each interval (for the second question)

• For 1950 - 1960: $\frac{20 - 11}{1960 - 1950}=\frac{9}{10} = 0.9$
• For 1960 - 1970: $\frac{38 - 20}{1970 - 1960}=\frac{18}{10}=1.8$
• For 1970 - 1980: $\frac{62 - 38}{1980 - 1970}=\frac{24}{10}=2.4$
• For 1990 - 2000: $\frac{101 - 92}{2000 - 1990}=\frac{9}{10}=0.9$

Answer:

For the first question: C. 1.8 million
For the second question: C. 1970 to 1980