the graph shows the depth of water at the end of a boat dock. a. find the amplitude of the graph. b. find…
the graph shows the depth of water at the end of a boat dock. a. find the amplitude of the graph. b. find the period of the function.
Answer
Explanation:
Step1: Identify maximum and minimum values
From the graph, the maximum depth $y_{max}=16$ feet and the minimum depth $y_{min}=10$ feet.
Step2: Calculate the amplitude
The formula for amplitude $A$ of a periodic - function is $A=\frac{y_{max}-y_{min}}{2}$. So, $A = \frac{16 - 10}{2}=\frac{6}{2}=3$ feet.
Step3: Identify the period
The period is the time it takes for the function to complete one full cycle. Looking at the graph, the function repeats itself every 12 hours.
Answer:
a. 3 feet b. 12 hours