SOLUTION: The average price of a gallon of gas in the us on January 1 2006 is $2.238 on Jan 1 2007 the price was $2.334 By what percent did the price increase from January 1 2006-2007? W

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Question 252912: The average price of a gallon of gas in the us on January 1 2006 is $2.238 on Jan 1 2007 the price was $2.334
By what percent did the price increase from January 1 2006-2007?
Write a formula giving the price of a gallon of gas in terms of the years following 2006 if prices continue to increase exponentially at the annual rate found in part a.
Use the formula to predict the year when the price of a gallon will reach $10
Found 2 solutions by drk, richwmiller:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
we want a percent change formula. It is
percent_change+=+100%2A%28end-start%29%2Fstart
we have 2 coordinates: (0,2.238) and (1,2.334).
percent_change+=+100%2A%282.334-2.238%29%2F2.238
percent_change+=+4.289544%
--
An exponential formula is:
A+=+p%2Ae%5E%28rt%29
A+=+2.238%2Ae%5E%28.04289544%2A%282006-t%29%29
---
10+=+2.238%2Ae%5E%28.04289544%2A%282006-t%29%29
divide both sides by 2.238 to get
4.46827+=+e%5E%28.04289544%2A%282006-t%29%29
take LN of both sides to get
1.497+=+.04289544%2A%282006-t%29
divide by .04289544 to get
34.89887+=+%282006-t%29
t+%7E+2040.89887
The price per gallon will reach $10 by late 2040.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
2.238-2.334=.096
.096/2.238=.04289=4.29%
There is no that this is an exponential increase
x(t)=p*4.29^(t/T)
where T is the part of the year (months)
and p=2.238
t is the number of years since 2006