Question

Kate decided to start a birdhouse business. It will cost her 600$ to start the business and 5$ to build each birdhouse. She sells the birdhouses for 15$ each.

1. What is the linear function that models Kate’s profit from her business?
2. What is the y-intercept of the function? What does that mean in this context?
3. What is this the slope of the function? What does that mean in this context?
4. How many birdhouses will Kate need to sell to earn at least 100$ in profit?

Answer 1

Step-by-step explanation: The linear function that models Kate’s profit from her business is given by P(x) = 15x - 5x - 600 where x is the number of birdhouses sold.

The y-intercept of the function is -600. In this context, it means that Kate will have a loss of $600 if she does not sell any birdhouses.

The slope of the function is 10. In this context, it means that Kate will earn $10 for each birdhouse sold.

To earn at least $100 in profit, Kate needs to sell at least (100 + 600)/(15 - 5) = 80 birdhouses.

Hope this helps! :)