Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 7; FL MA.912.C.5.2-C.5.4; CCSS.HSM; CCSS.MP1, MP2, MP4, MP5, MP6; Integrated Calculus II Standards CAL2-ODE; TEKS 19 TAC section 111.55

CAL2.83 Exponential Growth and Decay Models Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.83 Exponential Growth and Decay Models. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.83 Exponential Growth and Decay Models - Choose the correct solution, parameter interpretation, and prediction for dy/dt = ky. Standards: AP Calculus BC Unit 7; FL MA.912.C.5.2-C.5.4; CCSS.HSM; CCSS.MP1, MP2, MP4, MP5, MP6; Integrated Calculus II Standards CAL2-ODE; TEKS 19 TAC section 111.55.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Calculus II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related CAL2.83 Exponential Growth and Decay Models skill assessments:

Problem 1Difficulty: Mastery
A data set has y(0) = 10, y(1) = 20, and y(2) = 45. Can one constant-k model dy/dt = ky fit all three values exactly?
AYes, because all values are positive
BYes, with k = ln 45/2
CNo, because exponential models cannot increase
DNo, because the equal-interval multipliers 2 and 2.25 are not equal
Solution & Explanation:For a constant-k exponential model, equal time intervals must have the same multiplier. Here 20/10 = 2, but 45/20 = 2.25, so no single k fits all three exactly.
Problem 2Difficulty: Mastery
A graph of a positive solution of dy/dt = ky shows that y halves every 3 units of time. How long does it take y' to halve?
A6 units
Bln 2 units
C3 units
DIt never halves because y' is constant
Solution & Explanation:Because y' = ky, the derivative is multiplied by the same factor as y over any time interval. If y halves every 3 units, y' also halves every 3 units.
Problem 3Difficulty: Mastery
A solution of dy/dt = ky has y(0) = -10 and y(4) = -5. What is y'(4)?
A-5ln 2/4
B5ln 2/4
C-10ln 2
D5/4
Solution & Explanation:The ratio (-5)/(-10) = 1/2 over 4 units gives k = ln(1/2)/4 = -ln 2/4. Then y'(4) = ky(4) = (-ln 2/4)(-5) = 5ln 2/4.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Calculus II Math students. It aligns with educational standard AP Calculus BC Unit 7; FL MA.912.C.5.2-C.5.4; CCSS.HSM; CCSS.MP1, MP2, MP4, MP5, MP6; Integrated Calculus II Standards CAL2-ODE; TEKS 19 TAC section 111.55 (Choose the correct solution, parameter interpretation, and prediction for dy/dt = ky. Standards: AP Calculus BC Unit 7; FL MA.912.C.5.2-C.5.4; CCSS.HSM; CCSS.MP1, MP2, MP4, MP5, MP6; Integrated Calculus II Standards CAL2-ODE; TEKS 19 TAC section 111.55.).

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