standard_description: (+)Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
problem_activity: Task
Amy and Greg are raking up leaves from a large maple tree in their yard and Amy remarks "I'll bet this tree has a million leaves." Greg is skeptical. Amy suggests the following method to check whether or not this is possible:
Find a small maple tree and estimate how many leaves it has.
Use that number to figure out how many leaves the big maple tree has.
Describe the assumptions and calculations needed to carry for Amy's strategy.
Amy and Greg estimate that their maple tree is about $35$ feet tall. They find a $5$ foot tall maple tree and estimate that it has about $400$ leaves. Use your work from part (a) to estimate the number of leaves on Amy and Greg's tree.


aligns: no