IM Alg1.6.4 Practice: Comparing Quadratic and Exponential Functions
The table shows values of the expressions and . Describe how the values of each expression change as increases.
Predict which expression will have a greater value when: is 8
is 10
is 12
Find the value of each expression when is 8, 10, and 12 and fill out the table. Make an observation about how the values of the two expressions change as becomes greater and greater.
Function is defined by . Function is defined by . Which function is quadratic? Which one is exponential?
The values of which function will eventually be greater for larger and larger values of ?
The table shows the values of and for some values of .
Use the patterns in the table to explain why eventually the values of the exponential expression will overtake the values of the quadratic expression .
Here is a pattern of shapes. The area of each small square is 1 sq cm.
What is the area of the shape in Step 10?
What is the area of the shape in Step ?
Explain how you see the pattern growing.
A bicycle costs $240 and it loses of its value each year. Write expressions for the value of the bicycle, in dollars, after 1, 2, and 3 years.
When will the bike be worth less than $1?
Will the value of the bike ever be 0? Explain your reasoning.
This graph represents the inequality, , which describes the cost constraint in this situation. Let represent the number of acres of wheat and represent the number of acres of corn.
The inequality, represents the total area constraint in this situation. On the same coordinate plane, graph the solution to the inequality you wrote.Use the graphs to find at least two possible combinations of the number of acres of wheat and the number of acres of corn that the farmer could plant.
The combination of 400 acres of wheat and 700 acres of corn meets one constraint in the situation but not the other constraint. Which constraint does this meet? Explain your reasoning.