Question

Iver a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 4.35 ft at midnight, rises to a high of 8.3 ft, falls to a low of 0.4 ft, and then rises to 4.35 ft by the next midnight.
What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation?​

Answer 1

Answer:

$f(x)=3.95sin(\frac{\pi}{12}x)+4.35$

Step-by-step explanation:

Recall:

• Sinusoidal Function -> $f(x)=a*sin(bx+c)+d$
• Amplitude -> $a$

• Period -> $\frac{2\pi}{|b|}$
• Phase Shift -> $-\frac{c}{b}$

• Vertical Shift/Midline -> $d$

Given:

• Amplitude -> $a=8.3-4.35=3.95$
• Period -> $\frac{2\pi}{|b|}=\frac{2\pi}{|24|}=\frac{2\pi}{24}=\frac{\pi}{12}$
• Phase Shift -> $-\frac{c}{b}=-\frac{0}{24}=0$
• Vertical Shift/Midline -> $d=\frac{8.3+0.4}{2}=\frac{8.7}{2}=4.35$

Conclusion:

The equation that models the situation is $f(x)=3.95sin(\frac{\pi}{12}x)+4.35$

Hope this helped! I've attached a graph of the function so you can understand it better!