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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?

User Herms
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2 Answers

3 votes
-435.5m is the answer.
User Gopal Joshi
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1 vote

Answer:


  • 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.

User Shyam Bhagat
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