Data from local gas stations have revealed that gas prices decreased exponentially each week in late 2008. However there is debate over which model accurately describes the falling gas prices. Jim believes that the correct model for gas prices after x weeks is while April believes the model should be . What comparisons can be made about the two different models?
A) The gas prices decreased at a rate of 76% every week as opposed to 94% every week.
B) The gas prices decreased at a rate of 24% every week as opposed to 6% every week.
C) The price of the gas is $0.18 less than it was before.
D) The initial gas price decreased.
E) After x weeks the gas price is 0.76 times as much as the initial gas price instead of 0.94 times as much.

Question

Data from local gas stations have revealed that gas prices decreased exponentially each week in late 2008. However there is debate over which model accurately describes the falling gas prices. Jim believes that the correct model for gas prices after x weeks is  while April believes the model should be  . What comparisons can be made about the two different models?
A) The gas prices decreased at a rate of 76% every week as opposed to 94% every week. 
B) The gas prices decreased at a rate of 24% every week as opposed to 6% every week. 
C) The price of the gas is $0.18 less than it was before. 
D) The initial gas price decreased. 
E) After x weeks the gas price is 0.76 times as much as the initial gas price instead of 0.94 times as much.

Quizplus · Accepted Answer

Both models fit an exponential function with a base of e. The difference between the models is in the rate of decrease, which is the coefficient of the x term. The coefficient in Jim's model is -0.76 and in April's model it is -0.94. Therefore, the comparison between the two models is that the gas prices decreased at a rate of 24% every week as opposed to 6% every week.

Data from Local Gas Stations Have Revealed That Gas Prices