Chapter 13.1, Problem 22PPSE

Solution

i.

To find: The given statement can be represented as periodic function or not.

It can be represented as periodic function.

Given:

The statement that the average monthly temperature recorder every month for three years.

Calculation:

This statement can be represented as periodic function because the average monthly temperature is same from one year to next year. It means the temperature is repeating and it is understood that the curve of periodic function is symmetric and repeat itself.

Conclusion:

Hence, it can be represented as periodic function.

ii.

To find: The given statement can be represented as periodic function or not.

The given statement cannot be represented as periodic function.

Given:

The statement that population recorded of certain community recorded every year for the given time.

Calculation:

This cannot be represented as periodic function because the periodic function repeats itself, but the general observation is that population is increases from one year to next year and it is not repetitive.

Conclusion:

Hence, it cannot be represented as periodic function.

iii.

To find: The given statement can be represented as periodic function or not.

The given statement can be represented as periodic function.

Given:

The statement that car passes through an intersection recorded for two days.

Calculation:

This statement can be represented as a periodic function because the number of cars passes through intersection in two workdays are also same.

Conclusion:

Hence, it cannot be represented as periodic function.