Question

The PTA was doing a fundraiser and bought 500 megaphones to sell for a pep rally. The profit (p) from the sale of megaphones can be represented by: p(m) = 3.5m-875. Which of the following represents the range in the context of the situation?i. p(m) >= -875 where p(m) is all real numbersii. {-875,-871.5, -868, -864.5, ...875}iii. 0 <= m <= 500a. IIb. Ic. IIId. I, II

Answer 1

Since the profit equation has been given to us as

`p(m)=3.5m-875`

Where m is the number of megaphones sold.

Since m can only take integer values from zero and above.

When no megaphone was sold, p(m)=p(0)=-875

Therefore, the range is;

`p(m)\ge-875`

However p(m) is not all real numbers.

When 500 megaphones were sold, the profit is;

`3.5(500)-875=875`

This is the correct range.

Therefore, the range is represented as;

`\mleft\lbrace-875,-871.5,\ldots,875\mright\rbrace`

Thus the correct option is a. II