Solve exponential growth and exponential decay application problems.
?
?
?
?
?
Leo leaves his house one morning and notices a small plant growing in the yard that he has never noticed before. Out of curiosity, he grabs a ruler and measures it; the plant is 3 cm tall. Exactly one week later, Leo notices the plant has grown quite a bit, so he measures it again; now it is 9 cm tall. And one week after that, it measures 27 cm.
Leo knows that it is unlikely that the plant will continue to triple in height each week indefinitely, but he starts to wonder about the height of the plant before he started to measure it and how he could model its growth mathematically. Suppose that the plant follows a rule, “triples in height each week.”
Week | $${-4}$$ | $${-3}$$ | $${-2}$$ | $${-1 }$$ | $$0$$ | $$1$$ | $$2$$ | $$3$$ | $$4$$ | $$5$$ | $$w$$ |
Height (cm) | $$3$$ | $$9$$ | $$27$$ | ||||||||
Height Expression | $$3^2$$ | $$3^3$$ |
Predicting the Past, accessed on May 16, 2018, 4:51 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
?
The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
?
Mr. Miller starts working for a technology company this year. His salary the first year is $40,000. According to the company’s employee handbook, each following year Mr. Miller works at the company, he is eligible for a raise equal to 2–5% of his previous year’s salary.
Mr. Miller calculates the range of his raise on his first year’s salary. He adds that amount as his raise for each following year. Mr. Miller thinks that:
MAT.HS.ER.4.00FLE.E.566 from Development and Design: Item and Task Specifications made available by Smarter Balanced Assessment Consortium. © The Regents of the University of California – Smarter Balanced Assessment Consortium. Accessed May 18, 2018, 3:31 p.m..