Gasoline prices in Matthew's town have increased 18% each year for the past two years.
a.) Let g be the current price of a gallon of gas in Matthew's town. Write an equation that describes the projected price per gallon, p, at a time t years from now if this trend continues.
b.) Rewrite your equation to find the effective quarterly percentage increase, to the nearest hundredth of a percent.
Gasoline prices have risen 18% annually. Let g be the current price of a gallon of gasoline and t the number of years from now.
(a) What is the projected cost of gas t years from now?
We use the formula for compound interest. (Note that this is compounding since the new price of gas takes into account all of the previous period's price, not just the original price.)
A=P(1+r/n)^(nt) where A is the amount at time t, P is the original amount, r is the annual interest rate, n is the number of compounding periods per year, and t is time in years.
With P=g, r=.18 and n=1 we have A=g(1+.18)^t
The formula is A=g(1.18)^t
(b) To find the effective quarterly increase note that P=g, r=.18, n=4 and t=1
A=g(1+.18/4) so A=g(1+.045) or A=1.045g from one quarter to the next.