A community bird-watching society makes and sells simple bird feeders to raise money for its conservation activities. The materials for each feeder cost $5, and the society sells an average of 20 per week at a price of $9 each. The society has been considering raising the price, so it conducts a survey and finds that for every dollar increase, it loses 2 sales per week.

(a) Find a function that models weekly profit in terms of price per feeder. (Let x be the price per feeder and P(x) be the profit.)

Let the number of $1 increases be n

selling price now : 9
number sold now: 20

after increase....
selling price = 9+n
number sold = 20-2n

P(n) = (9+n)(20-2n) - 5(20-2n)

( change my variable to x )

To find a function that models weekly profit in terms of the price per feeder, let's define the variables:

x = price per feeder (in dollars)
P(x) = profit per week

We know that the cost of materials for each feeder is $5. Therefore, the profit per feeder can be calculated as:

Profit per feeder = Selling price per feeder - Cost of materials per feeder
= x - $5

The society sells an average of 20 feeders per week, so the total profit per week can be calculated as:

P(x) = Number of feeders sold per week * Profit per feeder
= 20 * (x - $5)
= 20x - $100

Therefore, the function that models the weekly profit in terms of the price per feeder is P(x) = 20x - $100.

To find a function that models weekly profit in terms of the price per feeder, we need to consider the cost and revenue involved.

The cost per feeder is given as $5, and the society sells an average of 20 feeders per week. So the total cost would be:

Cost = $5 x 20 = $100

The revenue per feeder is the price at which the feeders are sold. Let x represent the price per feeder. So the revenue for selling 20 feeders would be:

Revenue = x x 20 = 20x

The profit is the difference between revenue and cost:

Profit = Revenue - Cost

Profit = 20x - $100

Therefore, the function that models weekly profit in terms of the price per feeder is:

P(x) = 20x - $100