Question

An apple farmer has been researching his crop and has found that each of his trees will produce

300 apples on average. He currently has 100 apple trees. (1 point each)
a. Create a function that gives the amount of apples he will have this season if he plants × new trees.
b. Describe the domain of your function.
c. Describe the range of your function.

Answer 1

a. The function that gives the amount of apples the farmer will have this season if he plants "x" new trees can be defined as:

f(x) = 300 * (100 + x)

In this function, "x" represents the number of new trees the farmer plants, and 100 represents the initial number of apple trees he already has. The function calculates the total number of apples by multiplying the average number of apples per tree (300) by the total number of trees (100 + x).

b. The domain of the function is the set of all non-negative real numbers, as the farmer can plant any non-negative number of new trees. In mathematical notation, the domain can be represented as:

Domain: x ≥ 0

c. The range of the function is the set of all non-negative real numbers as well. Since the average number of apples per tree is positive (300), and the number of trees (100 + x) is always non-negative, the total number of apples will always be non-negative. In mathematical notation, the range can be represented as:

Range: f(x) ≥ 0