Thread: Trig Graph Equation

The water board of a local authority discovered it was able to represent the approximate amount of water W(t), in miilions of gallons, stored in a resevoir t months after 1st May 1988 by the formula W(t) = 1.1 - sin (pi t / 6)
The board then predicted that under normal conditions this formula would apply for three years.

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On the 1st of April 1990 a serious fire required an extra 1/4 million gallons of water from the resevoir to bring the fire under control. Assuming that the previous trends continues from the new lower lever, when will the resevoir run dry if water rationing is not imposed?

(sorry for the long read)

Answer = 28th June 1990

How do you work this out :S
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Thanks

Originally Posted by r_maths

The water board of a local authority discovered it was able to represent the approximate amount of water W(t), in miilions of gallons, stored in a resevoir t months after 1st May 1988 by the formula W(t) = 1.1 - sin (pi t / 6)
The board then predicted that under normal conditions this formula would apply for three years.

On the 1st of April 1990 a serious fire required an extra 1/4 million gallons of water from the resevoir to bring the fire under control. Assuming that the previous trends continues from the new lower lever, when will the resevoir run dry if water rationing is not imposed?

Answer = 28th June 1990

How do you work this out

Hello,

only a rough sketch of a possible solution (I haven't much time yet )

1. The function w(t) = 1.1 - sin((pi/6)*t) doesn't have any zeros.

2. 1. April 1990 correspond to w(23) = 8/5 (1.6*10^6 gallons)

3. After that date you deal with a new function:

a(t) = (1.1 - 0.25) - sin((pi/6)*t)

4. This function has a lot of zeros. Calculate the zero directly after t = 23

5. Good luck!

EB