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. (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 35 weeks. (4 points)

Answer 1

Answer:

  A. b(w) = 80w +30

  B. input: weeks; output: flowers that bloomed

  C. 2830

Step-by-step explanation:

Part A:

For f(s) = 2s +30, and s(w) = 40w, the composite function f(s(w)) is ...

  b(w) = f(s(w)) = 2(40w) +30

  b(w) = 80w +30 . . . . . . blooms over w weeks

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Part B:

The input units of f(s) are seeds. The output units are flowers.

The input units of s(w) are weeks. The output units are seeds.

Then the function b(w) above has input units of weeks, and output units of flowers (blooms).

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Part C:

For 35 weeks, the number of flowers that bloomed is ...

  b(35) = 80(35) +30 = 2830 . . . . flowers bloomed over 35 weeks