Question

A scientist observes that the planted trees grow at a rate inversely proportional to their height. If the original height of the trees were as given in the chart, find their average growth rate.


Assume that the growth rate and height are related in the form of
$y=\frac{1}{x}$

• A. $0.32$
• B. $0.25$
• C. $0.35$
• D. $0.22$

Answer 1

The correct option is A $0.32$

$\text{The growth rate of each tree is}inverselyproportional\text{to the tree's height.}$

$Growthrateofatree=\frac{1}{Height}$

Hence, we have:

$Tree$	$A$	$B$	$C$	$D$
$Growthrate$	$\frac{1}{2}$	$\frac{1}{3}$	$\frac{1}{4}$	$\frac{1}{5}$

$Sumofthegrowthrates=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{1\times 30}{2\times 30}+\frac{1\times 20}{3\times 20}+\frac{1\times 15}{4\times 15}+\frac{1\times 12}{5\times 12}=\frac{30}{60}+\frac{20}{60}+\frac{15}{60}+\frac{12}{60}=\frac{30+20+15+12}{60}=\frac{77}{60}$

Now, for four trees,
$Averagegrowthrate=\frac{77}{60}÷4\approx 0.32$