Question

The price of milk has been steadily increasing 5% per year. If the cost of a gallon is now $3.89: What will it cost in 10 years? What did it cost 5 years ago?

Answer 1

This is the concept of exponential growth; The rate of growth of the price milk is 0.05, current price=$ 3.89;
this information can be modeled by the exponential growth equation given by:
y=ae^(nr)
where;
a=initial value
r=rate of growth;
n=number of years
thus the function modeling our information will be:
y=3.89e^0.05n

the price after 10 years will be:
y=3.89e^(0.05*10)
y=3.89*1.649
y=6.41

the price after 10 years will be $ 6.41

The price 5 years ago will be:
y=3.89*e^(-5*0.05)
y=3.89 e^(-0.25)
y=3.03
thus we conclude that the price 5 years ago was $ 3.03