From an elevation of 3.5 m below the surface of the water, a northern bottlenose whale dives at a rate of -1.8 m/s. write a rule that gives the whale's depth d as a function of time in minutes. what is the whale's depth after 4 in?

Step-by-step explanation:

We want to find the depth d in function of time,  for a constant speed, this will take the form  

,

we know that at time t = 0 the whale its at 3,5 m below the surface, so we can write:

Now, the whale dives at a rate of -1.8 m/s, so the depth increases by 1.8 m/s this must be our b, but before putting it in our equation, we need to convert this to m/min, luckily, we know that one minute has 60 seconds, so :

,

dividing for 1 min of each side, we can get our conversion factor:

.

Then, we can multiply the whale dives rate for this conversion factor, we are allowed to do that cause the conversion factors equals 1:

We can put this in our equation for depht:

To find what is the depth after 4 min, we just take t = 4 min

,

,

,

So the whale's depth after 4 min will be 435.5 m.

this shows a reflection over the x-axis and is translated one unit down and 6 units to the right (x + 6, y - 1)

hope this !

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