On Dolphin Beach, the high tide is 1.8 meters and only occurs at 12 a. m. and 12 p. m. The low tide is 0.4 meter and only occurs at 6 a. m. and 6 p. m.

Which function models the height of the tide t hours after 12 a. m.?

h(t)=0.7cos(πt/6)+1.1

h(t)=1.8cos(πt/3)+0.4

h(t)=1.1sin(πt/3)+0.7

h(t)=0.7sin(πt/6)+1.1

h(t)=0.7sin(πt/6)+1.1

Step-by-step explanation:

A periodic function that models the height of the tide can be written as

where

A is the amplitude

is the angular frequency

is the central value of the tide

Here we know that:

- the hight tide is 1.8 meters

- the low tide is 0.4 meters

So, the central value of the tide is

Also, the amplitude is the maximum displacement from the equilibrium position (central value of the tide), so:

Now we have to find the angular frequency, which is related to the period T by

Here the high tide occurs at 12 am and 12 pm: this means that the period is 12 hours, so

T = 12

Therefore, the correct equation is

h(t)=0.7sin(πt/6)+1.1

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