Question

Use the information below to answer questions 34-35 The volume of water in the lake is 150,000 Kilolitres. The volume kept decreasing at the rate of 45% every monthly through evaporation and a river outlet. 34. How long will it take before there is only 15,000 Kilolitres left in the lake? A. 4.5 months B. 6 months C. 300 months D. 75 months
how many more months will if take the lake to dry up the same descrese rate?
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Answer 1

If the volume of the river is 150000 kilolitres and 45% is evaporating every month then after 4.5 months there will be 15000 kilolitres and it will take approximately 42 months to completely dry up.

Given that the volume of the river is 150000 kilolitres and the water is decreasing at a rate of 45%.

We are required to find the number of months after which the water left in the river will be 15000 kilolitres and the number of months after which the river will be completely dried up.

The amount of water  left after n years can be written as:

=150000*$(1-0.45)^{n}$

When the volume will be 15000 kilolitres.

15000=150000*$(0.55)^{n}$

0.1=$(0.55)^{n}$

$(0.55)^{4.5}$=$(0.55)^{n}$

By comparing both sides we will get n=4.5.

Now put the amount of volume be 0.

0=150000*$(0.55)^{n}$

$(0.55)^{42}$=$(0.55)^{n}$

By equating both sides we will get n=42. We know that 0.55 to the power anything will not give 0 but we have taken nearest value to 0.

Thus the lake will take 42 months to completely dried up.

Hence if the volume of the river is 150000 kilolitres and 45% is evaporating every month then after 4.5 months there will be 15000 kilolitres and it will take approximately 42 months to completely dry up.

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