SOLUTION: More cities are supplying some of their fresh water through desalination, the process of removing salt from the ocean water. The worldwide desalination capacity has grown exponent

Question 328596: More cities are supplying some of their fresh water through desalination, the process of removing salt from the ocean water. The worldwide desalination capacity has grown exponentially from 15 million m^3 per day in 1990 to 55 million m^3 per day in 2007. predict the worldwide desalination capacity in 2012.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Exponentially usually means y = x * (1+g)^n

y = future
x = present
g = growth rate
n = number of time period usually expressed in year but not necessarily.

You are given that the growth was 15 in 1990 to 55 in 2007.

The units are million cubic meters I believe.

The answer will be correct regardless of what the unit of measure as long as they are consistent.

You went from 15 in 1990 to 55 in 2007.

This means that the equation of y = x * (1+g)^n becomes:

y = 55
x = 15
n = 2007 - 1990 = 17
g needs to be found.

The equation becomes:

55 = 15 * (1+g)^17

Divide both sides of the equation by 15 to get:

55/15 = (1+g)^17

Take the log of both sides of this equation to get:

log(55/15) = log((1+g)^17)

Since log(a^b) = b*log(a), this equation becomes:

log(55/15) = 17*log(1+g)

Divide both sides of this equation by 17 to get:

log(55/15)/17 = log(1+g)

Solve for log(55/15)/17 to get:

.033192437 = log(1+g)

Take the anti-log of .033192437 to get:

1.079424912 = 1 + g

Subtract 1 from both sides of the equation to get:

.079424912 = g

That's your annual growth rate in fresh water being supplied through desalinization.

To confirm, Take 15 * (1.07)^17 to get 55

The equation is confirmed as good.

To predict the amount of water being supplied through desalinization in 2012, then use the same formula in either of the following ways. Either way you should get the same answer.

First way:

2012 - 1990 = 22

15 * 1.079424912 ^ 22 = 80.59811317

Second way:

2012 - 2007 = 5

55 * 1.079424912 ^ 5 = 80.59811317

Your answer is that 80.59811317 million cubic meters of water will be supplied through desalinization in the year 2012 if the average growth rate per year holds.

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