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A lost turtle - swimming 13 feet below the surface of the water - begins to ascend at 0.5 foot per second. In hopes of (harmlessly) capturing the turtle, a diver jumps into the water to a depth of 4 feet before descending at a rate of 0.25 foot per second.

a) Write an equation to model the position of the turtle at any given time.



b) Write an equation to model the position of the diver at any given time.



c) After how long will the diver be able to catch the turtle?



d) At what depth will the diver be able to catch the turtle?

Respuesta :

sqdancefan

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Answer:

  a) T(t) = -13 +0.5t

  b) D(t) = -4 -0.25t

  c) 12 seconds

  d) 7 feet

Step-by-step explanation:

a) The turtle starts at -13 feet and increases its elevation relative to the water's surface by 0.5 ft/second. After t seconds, the turtle will be 0.5t feet closer to the surface, so its depth will be ...

 T(t) = -13 +0.5t

__

b) The diver starts at -4 feet and decreases their elevation relative to the water's surface by 0.35 ft/second. After t seconds, the diver will be 0.25t lower than the initial position, so their depth will be ...

  D(t) = -4 -0.25t

__

c) The diver and turtle will be at the same depth when ...

  T(t) = D(t)

  -13 +0.50t = -4 -0.25t

  0.75t = 9 . . . . . . . . . . . . add 13+0.25t

  t = 12 . . . . . . . . . . . . . . . divide by 0.75

The diver and turtle will be at the same depth after 12 seconds.

__

d) That depth will be ...

  T(12) = -13 +0.5(12) = -13 +6 = -7

The diver and turtle meet at a depth of 7 feet.

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