Question

A tank continuously drains so that the volume V of water (in gallons) remaining in the tank after t minutes is V(t) = 100(1-((t)/20))

a) What is the domain of V(t)by the context of the problem? What is the range?

Domain: [0, 20], Range: [0, 100]

Domain: [0, 100], Range: [0, 20]

Domain: [100, ?], Range: [20, ?]

Domain: [20, ?], Range: [100, ?]

Domain: [0, 100], Range: [0, 100]


(b) What is implied about the physical nature of the problem that ensures

V(t) is one-to-one on its domain? Find the inverse function. (Enter V(t) as just V.)
t =

(c) What is V ?1(4)?

Answer 1

Answer:

(t) = Domain is all the values t can take. From the equation we find that 20-t>=0 as V cannot be negative. Hence t <=20. a…

Answer 2

Answer:

a)Domain = [0,20]

b) t = 20- V(t)/5

c) 19.2 minutes

Step-by-step explanation:

V(t)= 5(20-t)

Domain is all the values t can take.

From the equation we find that 20-t>=0 as V cannot be negative.

Hence t <=20. also t cannot be negative.

Domain = [0,20]

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When t=20, V = 0 and when t =0 V =100

Range = [0,100]

Domain: [0, 20], Range: [0, 100] I option is right

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V is one to one because if V(t1) = V(t2) then

5(20-t1)=5(20-t2)   ---> t1=t2

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V(t) = 5(20-t)

t = 20- V(t)/5

also $V^{-1}$ =20-V(t)/5

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V inverse of 4 = 20-(4/5)=19.2 min