Answer:
- [tex]d(t) = \ 3.5 \ m \ + \ - \ 108 \ \frac{m}{min} \ * \ t [/tex]
- The whale's depth after 4 min will be 435.5 m.
Step-by-step explanation:
We want to find the depth d in function of time, for a constant speed, this will take the form
[tex]d(t) \ = \ a \ + \ b \ * \ t[/tex],
we know that at time t = 0 the whale its at 3,5 m below the surface, so we can write:
[tex]d \ (0) \ = \ a \ + \ b \ * 0 = \ 3.5 \ m[/tex]
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 :
[tex]1 \ min \ = \ 60 \ s[/tex],
dividing for 1 min of each side, we can get our conversion factor:
[tex]\frac{1 \ min}{1 \ min} \ = \ \frac{60 \ sec}{60 \ 1 \ min}[/tex]
[tex]\frac{60 \ s}{1 \ min} \ = \ 1[/tex].
Then, we can multiply the whale dives rate for this conversion factor, we are allowed to do that cause the conversion factors equals 1:
[tex] \ 1.8 \ \frac{m}{s} \ * \ 60 \ \frac{s}{min} [/tex]
[tex] \ 108 \ \frac{m}{min}[/tex]
We can put this in our equation for depht:
[tex]d(t) = \ 3.5 \ m \ + \ 108 \ \frac{m}{min} \ * \ t [/tex]
To find what is the depth after 4 min, we just take t = 4 min
[tex]d( 4 min) = \ 3.5 \ m \ + \ 108 \ \frac{m}{min} \ * \ 4 min [/tex],
[tex]d( 4 min) = \ 3.5 \ m \ + \ 432 \ m [/tex],
[tex]d( 4 min) = \ 435.5 \ m [/tex],
So the whale's depth after 4 min will be 435.5 m.
