A1.F-LE.A.3
Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically.
Example Problems
Maria and Lucia own land.
Lucia began with 11 hectares during the first month, and gained 5 more hectares each month.
Maria owned 6 hectares during the first one, and her land multiplied by a factor of each month.
After which month will Maria's amount of land first exceed Lucia's amount of land?
Lucia began with 11 hectares during the first month, and gained 5 more hectares each month.
Maria owned 6 hectares during the first one, and her land multiplied by a factor of each month.
After which month will Maria's amount of land first exceed Lucia's amount of land?
Eva and Tom own land.
Tom started with 13 hectares in the first month, gaining 6 more hectares each subsequent month.
Eva owned 8 hectares in the first month, and her land multiplied by a factor of 1.5 each month.
After which month will Eva's amount of land first exceed Tom's amount of land?
Tom started with 13 hectares in the first month, gaining 6 more hectares each subsequent month.
Eva owned 8 hectares in the first month, and her land multiplied by a factor of 1.5 each month.
After which month will Eva's amount of land first exceed Tom's amount of land?
Rebecca made two investments:
Fund U has a value of $900 in the first year and increases by $75 each subsequent year.
Fund V has a value of $850 in the first year and grows by 9% per year.
Rebecca checks the value once a year, at the end of the year.
What is the first year in which V exceeds U?
Fund U has a value of $900 in the first year and increases by $75 each subsequent year.
Fund V has a value of $850 in the first year and grows by 9% per year.
Rebecca checks the value once a year, at the end of the year.
What is the first year in which V exceeds U?
Khan Academy Resources
1-on-1 AI tutoring aligned to A1.F-LE.A.3. Instant help for students, real-time insights for teachers.
Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.
Free for teachers, forever →