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Exponential Function Decay (Continuous) - Equation to Scenario

Level 1

This topic focuses on the application of exponential decay functions in continuous scenarios. Students are presented with a series of problem statements requiring them to match scenarios to given exponential decay equations. The scenarios generally involve populations of organisms or concentrations of substances decreasing over time due to a continuous percentage change. Each problem provides an equation and two potential real-world contexts, such as declining populations of whales or bacteria, or decaying concentrations of radioactive materials or toxins. Students must identify which scenario accurately reflects the equation.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Exponential Function Decay (Continuous) - Equation to Scenario Worksheet

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Exponential Function Decay (Continuous) - Equation to Scenario
1
Which scenario describes this equation?
A LaTex expression showing 596 =700 times e to the power of (-0.02 times 8)
a
A whale population starts at 700. It declines continuously at 2% per year. After 8 years it has decreased to a population of 596 whales.
b
A whale population starts at 800. It declines continuously at 2% per year. After 7 years it has decreased to a population of 596 whales.
2
Which scenario describes this equation?
A LaTex expression showing 723 =800 times e to the power of (-0.05 times 2)
a
A bacteria population starts at 200. It declines continuously at 5% per year. After 8 years it has decreased to a population of 723 bacteria.
b
A bacteria population starts at 800. It declines continuously at 5% per year. After 2 years it has decreased to a population of 723 bacteria.
3
Which scenario describes this equation?
A LaTex expression showing 532 =600 times e to the power of (-0.03 times 4)
a
A whale population starts at 600. It declines continuously at 3% per quarter. After 4 quarters it has decreased to a population of 532 whales.
b
A whale population starts at 400. It declines continuously at 3% per quarter. After 6 quarters it has decreased to a population of 532 whales.
4
Which scenario describes this equation?
A LaTex expression showing 123 =200 times e to the power of (-0.06 times 8)
a
A radioactive material starts at an isotope concentration of 200ppm. It decays continuously at 6% per day. After 8 days it has decayed to an isotope concentration of 123ppm.
b
A radioactive material starts at an isotope concentration of 600ppm. It decays continuously at 2% per day. After 8 days it has decayed to an isotope concentration of 123ppm.
5
Which scenario describes this equation?
A LaTex expression showing 159 =300 times e to the power of (-0.09 times 7)
a
A whale population starts at 300. It declines continuously at 9% per year. After 7 years it has decreased to a population of 159 whales.
b
A whale population starts at 900. It declines continuously at 3% per year. After 7 years it has decreased to a population of 159 whales.
6
Which scenario describes this equation?
A LaTex expression showing 217 =300 times e to the power of (-0.04 times 8)
a
A radioactive material starts at an isotope concentration of 800ppm. It decays continuously at 4% per day. After 3 days it has decayed to an isotope concentration of 217ppm.
b
A radioactive material starts at an isotope concentration of 300ppm. It decays continuously at 4% per day. After 8 days it has decayed to an isotope concentration of 217ppm.
7
Which scenario describes this equation?
A LaTex expression showing 486 =600 times e to the power of (-0.03 times 7)
a
A toxin starts at a concentration of 600mg/L. It declines continuously at 3% per hour. After 7 hours it has decreased to a concentration of 486mg/L.
b
A toxin starts at a concentration of 300mg/L. It declines continuously at 6% per hour. After 7 hours it has decreased to a concentration of 486mg/L.
8
Which scenario describes this equation?
A LaTex expression showing 361 =400 times e to the power of (-0.02 times 5)
a
A bacteria population starts at 500. It declines continuously at 2% per day. After 4 days it has decreased to a population of 361 bacteria.
b
A bacteria population starts at 400. It declines continuously at 2% per day. After 5 days it has decreased to a population of 361 bacteria.