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stiks02 [169]
3 years ago
11

A 1000 gallon tank, initially full of water, develops a leak at the bottom. Given that 300 gallons of water leak out in the firs

t 30 minutes, find the amount of water, A(t), left in the tank t minutes after the leak develops if the water drains off at a rate proportional to the amount of water present.
a. A(t)= 1000(1/3)^1/10t
b. A(t)= 1000(1/2)^-1/10t
c. A(t)= 1000(1001/2)^t
d. A(t)= 1000e ^-1/10t
e. A(t)= 1000(1/2)^1/10t
f. None of these
Mathematics
1 answer:
Over [174]3 years ago
6 0

Answer:

option F

Step-by-step explanation:

given,

capacity of tank = 1000 gallon

volume of water leak = 300 gallon

time = 30 min

water is leaking at the rate

formula used

A = B e^{-kt}

At t = 0   A = 1000 gallons

1000= B e^{-k\times 0}

B = 1000

A = 1000 e^{-kt}

at t = 30        A  = 700

700= 1000 e^{-k\times 30}

e^{-k\times 30}=0.7

taking ln both side

-k\times 30=ln(0.7)

k=-\dfrac{ln(0.7)}{30}

now,

A = 1000 e^{\dfrac{ln(0.7)}{30}t}

A = 1000\times 0.7 e^{\dfrac{t}{30}}

A = 700 e^{\dfrac{t}{30}}

hence, the correct answer is option F

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