A new store has opened up in the mall. A pencil is originally priced at $1.00. Every year after its initial launch, the price of the pencil increases by $0.20. A book at the same store also initially cost $1.00. Every year, its price has doubles.
Constant Rate and Constant Percent Rate per Unit
The constant rate is the change between two terms. In this case, the constant rate would be 0.2 because every year, the pencil cost $0.20 more.
The constant percent rate per unit is the common ratio that each term increases or decreases by. In this word problem, it would be 200% because as each year passes, the book costs twice as much.
The constant percent rate per unit is the common ratio that each term increases or decreases by. In this word problem, it would be 200% because as each year passes, the book costs twice as much.
Graphs
f(x) = 0.20x + 1
f(x) = 2^x*1
Compare the Linear and Exponential Models
The linear model increased by a steady rate of 0.20 every unit. However, the exponential model had a common ratio of 2 meaning each term was twice the previous one and had no set amount of increase.
The linear model and the exponential model both had a y-intercept or base amount of 1.
The linear model and the exponential model both had a y-intercept or base amount of 1.
Parameters
The parameter in the linear model is the rate in which the price of the pencil increases or 0.20 and the starting cost which is 1.
The parameter in the exponential model is the common ratio in which the cost of the book increases which is 2 and the starting cost which is 1.
The parameter in the exponential model is the common ratio in which the cost of the book increases which is 2 and the starting cost which is 1.