Lesson 5 The Tortoise and the Hare Solidify Understanding
Which function has the greatest average rate of change in the interval given?
Compare quadratic and exponential functions.
Determine which type of function, quadratic or exponential, grows faster in a given interval.
How does the growth of a quadratic function compare to the growth of an exponential function?
How can tables, graphs, and equations help to understand how quadratic and exponential functions grow?
Open Up the Math: Launch, Explore, Discuss
In the children’s story of the tortoise and the hare, the hare mocks the tortoise for being slow. The tortoise replies, “Slow and steady wins the race.” The hare says, “We’ll just see about that,” and challenges the tortoise to a race. The distance from the starting line of the hare is given by the function:
Because the hare is so confident that he can beat the tortoise, he gives the tortoise a
At what time does the hare catch up to the tortoise?
If the race course is very long, who wins: the tortoise or the hare? Why?
At what time(s) are they tied?
If the race course were
Use the properties
Ready for More?
In the case of the tortoise and the hare, the exponential function exceeded the quadratic function for large values of
Shape of Graph:
Rate of Change:
In this lesson we compared quadratic and exponential functions. We learned that in some intervals for small values of
Determine whether each representation is a function or not a function. If it is not a function describe what you would do to change it to make it a function.
State the domain and range of each graph. Use interval notation where appropriate.