Exponential Function Decay (Continuous) - Scenario to Equation

Level 1

These problems focus on creating exponential decay equations from scenarios involving continuous decay rates. Each scenario specifies an initial quantity (such as isotope concentration or bird population), a continuous percent rate of decay, and the remaining quantity after a certain period (hours, days, quarters, or years). Students are tasked with selecting the correct exponential function that matches these criteria, and the functions are presented in formats like \( P = P_0 \cdot e^{kt} \), where \( P_0 \) is the initial quantity, \( k \) is the decay rate, and \( t \) is the time.

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

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Exponential Function Decay (Continuous) - Scenario to Equation Worksheet

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Exponential Function Decay (Continuous) - Scenario to Equation
1
A radioactive material starts at an isotope concentration of 700ppm. It decays continuously at 2% per hour. After 8 hours it has decayed to an isotope concentration of 596ppm.
Which equation describes this scenario?
a A LaTex expression showing 596 =700 times e to the power of (-0.02 times 8)
b A LaTex expression showing 596 =200 times e to the power of (-0.07 times 8)
c A LaTex expression showing 596 =700 times e to the power of (-0.08 times 2)
d A LaTex expression showing 596 =800 times e to the power of (-0.02 times 7)
2
A radioactive material starts at an isotope concentration of 200ppm. It decays continuously at 7% per day. After 5 days it has decayed to an isotope concentration of 140ppm.
Which equation describes this scenario?
a A LaTex expression showing 140 =500 times e to the power of (-0.07 times 2)
b A LaTex expression showing 140 =200 times e to the power of (-0.07 times 5)
3
A radioactive material starts at an isotope concentration of 400ppm. It decays continuously at 6% per hour. After 2 hours it has decayed to an isotope concentration of 354ppm.
Which equation describes this scenario?
a A LaTex expression showing 354 =200 times e to the power of (-0.06 times 4)
b A LaTex expression showing 354 =400 times e to the power of (-0.02 times 6)
c A LaTex expression showing 354 =400 times e to the power of (-0.06 times 2)
4
A bird population starts at 200. It declines continuously at 5% per quarter. After 7 quarters it has decreased to a population of 140.
Which equation describes this scenario?
a A LaTex expression showing 140 =200 times e to the power of (-0.05 times 7)
b A LaTex expression showing 140 =700 times e to the power of (-0.05 times 2)
c A LaTex expression showing 140 =500 times e to the power of (-0.02 times 7)
d A LaTex expression showing 140 =200 times e to the power of (-0.07 times 5)
5
A bird population starts at 300. It declines continuously at 9% per quarter. After 6 quarters it has decreased to a population of 174.
Which equation describes this scenario?
a A LaTex expression showing 174 =600 times e to the power of (-0.09 times 3)
b A LaTex expression showing 174 =300 times e to the power of (-0.06 times 9)
c A LaTex expression showing 174 =300 times e to the power of (-0.09 times 6)
d A LaTex expression showing 174 =900 times e to the power of (-0.03 times 6)
6
A bird population starts at 600. It declines continuously at 2% per year. After 5 years it has decreased to a population of 542.
Which equation describes this scenario?
a A LaTex expression showing 542 =500 times e to the power of (-0.02 times 6)
b A LaTex expression showing 542 =600 times e to the power of (-0.02 times 5)
c A LaTex expression showing 542 =600 times e to the power of (-0.05 times 2)
7
A radioactive material starts at an isotope concentration of 800ppm. It decays continuously at 9% per hour. After 2 hours it has decayed to an isotope concentration of 668ppm.
Which equation describes this scenario?
a A LaTex expression showing 668 =200 times e to the power of (-0.09 times 8)
b A LaTex expression showing 668 =800 times e to the power of (-0.09 times 2)
c A LaTex expression showing 668 =900 times e to the power of (-0.08 times 2)
8
A bird population starts at 200. It declines continuously at 4% per year. After 5 years it has decreased to a population of 163.
Which equation describes this scenario?
a A LaTex expression showing 163 =200 times e to the power of (-0.04 times 5)
b A LaTex expression showing 163 =400 times e to the power of (-0.02 times 5)
c A LaTex expression showing 163 =500 times e to the power of (-0.04 times 2)