Question 4 (Essay Worth 10 points)
(06.05 MC)

Iris is a botanist who works for a garden that many tourists visit. The function f(s) = 2s + 25 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w) = 25w represents the number of seeds she plants per week, where w represents the number of weeks.

Part A: Write a composite function that represents how many flowers Iris can expect to bloom over a certain number of weeks. (4 points)

Part B: What are the units of measurement for the composite function in Part A? (2 points)

Part C: Evaluate the composite function in Part A for 30 weeks. (4 points)

A function is said to be a composite function when a function is written in another function. The composite function that represents the number of flowers is [tex]f(w) = 50w + 25[/tex] and the number of flowers for 30 weeks is 1525.

Given that:

[tex]f(s) = 2s + 25[/tex]

[tex]s(w) = 25w[/tex]

The number of flowers to bloom over w weeks is calculated using the following composite function: f(w)

[tex]f(s) = 2s + 25[/tex]

Replace s with s(w)

[tex]f(s(w)) = 2(s(w)) + 25[/tex]

Substitute [tex]s(w) = 25w[/tex]

[tex]f(s(w)) = 2(25w) + 25[/tex]

[tex]f(s(w)) = 50w + 25[/tex]

Hence:

[tex]f(w) = 50w + 25[/tex]

The units of the measurement of f(w) is flowers

The number of flower for 30 weeks means:

[tex]w = 30[/tex]

So, we have:

[tex]f(30) = 50 \times 30 + 25[/tex]

[tex]f(30) = 1525[/tex]

Hence, the number of flowers for 30 weeks is 1525