Question

Lily is a botanist who works for a garden that many tourists visit. The function f(s)=2s+30 represents the number of flowers that bloomed, where s is the number of seeds she planted. The function s(w)=40w 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 Lily can expect to bloom over a certain number of weeks.

a)f(s(w))=2(40w)+30
b)f(s(w))=2(40w+30)
c)f(s(w))=2(40w)+30w
d)f(s(w))=2(40w)+30

Answer 1

The composite function that represents the number of flowers Lily can expect to bloom over a certain number of weeks is f(s(w))=2(40w)+30. To form this function, substitute the seed function s(w) into the flower blooming function f(s), resulting in the correct option a).

Step-by-step explanation:

The problem involves creating a composite function to represent the number of flowers that will bloom based on the number of weeks Lily plants seeds. The first step is to substitute s(w) into f(s). This results in f(s(w))=f(40w). We can then apply the function f(s) = 2s + 30 to this value of s, which gives us f(s(w))=2(40w)+30, representing the number of flowers blooming over a certain number of weeks. Therefore, the correct answer is a) f(s(w))=2(40w)+30.

Let's break it down in more depth: First, s(w) = 40w gives us the number of seeds planted each week. We then use f(s) = 2s + 30 to calculate the flowers that bloom from those seeds. By substituting 40w for s in f(s), we get f(40w) which can be more explicitly written as 2(40w) + 30, which simplifies to 80w + 30. This is how the composite function is formed showing the dependent relationship between weeks and the number of flowers that bloom.