Math 1 · Unit 9 · Lesson 3 · part 4 of 5
A fraction ratio, and what f(3) = 50 means
A decay example, written in function notation.
A fraction ratio, and what f(3) = 50 means
A decay example, written in function notation. A medicine starts at 400 milligrams and half of it is left after each hour:
f(x) = 400 · (12)x
Here x counts the halvings, starting at 0. f(0) = 400, f(1) = 200, f(2) = 100, f(3) = 50.
What does f(3) = 50 mean?Read the input and the output in the story's words. The input 3 is the number of halvings (3 hours). The output 50 is what is left. So f(3) = 50 means: after 3 halvings, 50 milligrams are left. Check: 400 · (12)3 = 400 · 18 = 50.
A fraction ratio shrinks the terms, but never to 0. Half of a positive number is still a positive number. 50, 25, 12.5, 6.25: smaller every time, never 0. As a list starting at a1 = 400, the same sequence is an = 400 · (12)n − 1.