Question

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?

Answer 1

-435.5m is the answer.

Answer 2

• 
  `d(t) = \   3.5 \ m \ +  \ - \ 108 \ (m)/(min) \ * \ t`
• The whale's depth after 4 min will be 435.5 m.

Explanation:

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

`d(t) \ = \ a \ + \ b \ * \ t`,

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

`d \ (0) \ = \ a \ + \ b \ * 0 =  \ 3.5 \ m`

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 :

`1 \ min \ = \ 60 \ s`,

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

`(1 \ min)/(1 \ min) \ = \ (60 \ sec)/(60 \ 1 \ min)`

`(60 \ s)/(1 \ min) \ = \ 1`.

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

`\ 1.8 \ (m)/(s) \ * \ 60 \ (s)/(min)`

`\ 108 \ (m)/(min)`

We can put this in our equation for depht:

`d(t) = \ 3.5 \ m \ + \ 108 \ (m)/(min) \ * \ t`

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

`d( 4 min) = \ 3.5 \ m \ + \ 108 \ (m)/(min) \ * \ 4 min`,

`d( 4 min) = \ 3.5 \ m \ + \ 432 \ m`,

`d( 4 min) = \ 435.5 \ m`,

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