Question

 

In this project you are given the task of estimating the number of trees that will maximize the fruit production per acre of a local orchard. By researching other orchards, you discover that at 400 trees per acre, each tree will produce an average of 30 pounds of fruit. For each tree that is added to the acre, the average production per tree goes down 0.05 pounds

1. Use the information to build a table of values for this situation. Let t be the number of trees (above 400) planted per acre and find the total amount of fruit each acre will produce. Find at least eight sets of values. (Hint: You should add 20 trees at a time to obtain your values.)

2. Create a scatterplot using the values you found in the table on the calculator or computer and print it out.

3. Find a QUADRATIC function for the total production per acre when t trees over 400 are planted per acre.

4. Find the total production per acre when 400 trees are planted.

5. Estimate how many trees per acre should be planted per acre to produce 12,400 pounds of fruit.

6. Find the number of trees per acre that will maximize fruit production.

7. Find a reasonable domain and range for your model.

Answer 1

For Question 2, see the following scatter plot:

For Questions 1, 3, 4, 5, 6, 7, see solutions in images below.