Question

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?

Answer 1

Answer:

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:

$f(x)=A\.(1-r)^x$

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:

$f(x)=16.5\.(1-0.041)^x$

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:

$f(29)=16.5\,(1-0.041)^{29}=4.9 \,\, gallons$

Answer 2

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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