The total gallons of juice each person consumes a yearly has decreased 4.1% each year. In 1981 each person drink 16.5 gallons of juice on average. What was the approximate amount consumed per person in 2010?

The approximate amount consumed per person in 2010 is  4.9 gallons.

The formula that would used to determine the average gallon of juice consumed in 2010 is:  

FV = P (1 - r)^n

FV = Future value  

P = Present value = 16.5 gallons  

R = rate of decrease = 4.1%  

N = number of years = 2010 - 1981 = 29

16.5 x (1 - 0.041)^29  = 4.9 gallons

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The approximate number of gallons consumed by a person in 2010 will be 4.9 gallons

Step-by-step explanation:

Recall that the formula for exponential decrease is given by a function of the form:

where A is the initial value, r is the rate of decrease, and x is the time elapsed.

In our case, the initial value of gallons of juice per person (at the starting time = 1981) is 16.5 gallons. So A = 16.5 gallons.

the rate of decrease "r" is the decimal form of: 4.1%, that is r = 0.041

So we have:

Now we can calculate what the average number of gallons would be in the year 2010, knowing that between 1981 and 2010 there is an elapsed time in years of: 2010-1981 = 29 years. Then:

x = 17

step-by-step explanation:

1st step: isolate x.

24 - 3x = -27

-24         -24

-3x   =   -51

2nd step: divide.

-3x     =   -51

  3             3

  x       =     17

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step-by-step explanation:

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