Question

Cost of a balloon is inversely proportional to number of balloons purchased. Comment on the relationship of the rate of reaction with time.

• A. Cost of a balloon is a function of number of balloons purchased.
• B. From the defination of a function, the relationship between the cost of balloon and number of balloons purchased is not a function.
• C. The relationship is non-linear.
• D. The relationship is linear as the exponent of the variables is $1.$

Answer 1

Answer: (A), (C)

The relationship is non-linear.

Let the cost of a balloon is represented as $C$ unit and number of balloons purchased be $n.$
Here, $n$ is the independent variable.
Cost of a balloon is inversely proportional to number of balloons purchased.
$\Rightarrow C\propto \frac{1}{n}$
$\Rightarrow C=k\frac{1}{n}$
where $k$ is a constant of proportionality.
$\Rightarrow C=k{n}^{-1}$

The exponent of the independent variable is $-1.$
Hence, this is a non-linear function.