“Eggcelent”: Part I (10 min)
Assume that at the end of 2000, a dozen eggs cost 89 cents. Also assume that prices
rise 5% each year. In a situation like this, the figure 5% is called the rate of inflation.
1. How much did a dozen eggs cost at the end of 2001?
.9345 cents
2. How much did the price go up during 2001?
.9345 - .89 = .0445 cents
*ONCE THEY HAVE MASTERED THIS: GO TO QUESTION 3
Discussion (5-10 min)
*MISCONCEPTION: adding 5% to the cost of eggs each year that goes by okay for 1 &
2, not 3 & 4
*TRANSITION: multiply by 1.05% each yearhelps develop an equation
HINTS: “After one year, the price becomes what percentage of the original price?”
HINTS: Express the result of adding 5% in algebraic terms. For instance: “What would
the price be after a year if it started at x dollars?
If students write as: x+.05x, ask “How can you simplify this?”
“Eggcelent”: Part II (15-25 min)
Gather similar information for other years, until you think you understand what’s
happening. Then answer these questions, assuming the 5% inflation rate continues.
1. How much will a dozen eggs cost at the end of 2100? Explain your answer.
Discuss P=.89*1.05t for the price after t yearsBe sure students understand
that this equation is based on the fact that adding 5% to the price is equivalent
to multiplying it by 1.05.
*The price of a dozen eggs in year 2100 (after 100 years) is about $117.04
*Have students write an equation that could be used to answer question 4
2. In what year will a dozen eggs first cost over $100.
.89*1.05t = 100
*The price will first go over $100 in 97 years, that is, in year 2097
Discussion (5-10 min)
Based on the equation P= .89*1.05t, what kind of function is this?
*Review the term exponential The variable is the exponent (JACOB’S PUN)
What would the graph of the function look like?
Graph y = .89*1.05x on calculators to verify ideas