Exponential Function Decay (Continuous) - Equation and Scenario to Specific Value

Level 1

This math topic focuses on understanding and applying exponential function decay in continuous scenarios. Students practice solving questions related to the rate of decay, the duration of the decay process, and computing the initial and final values (like concentrations or populations) using exponential equations. It covers a variety of scenarios including bacterial population decline, whale population decline, and the reduction of toxic concentration levels. Additionally, there is a mix of problems requiring calculations of rate, time, and initial and final measurements, deepening students' grasp of exponential functions in real-world contexts.

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

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Exponential Function Decay (Continuous) - Equation and Scenario to Specific Value Worksheet

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Exponential Function Decay (Continuous) - Equation and Scenario to Sp...
1
What is the rate in this equation for a a continuously declining bacteria population?
A LaTex expression showing 263 =400 times e to the power of (-0.07 times 6)
a A LaTex expression showing r = 400\%
b A LaTex expression showing r = 7\%
c A LaTex expression showing r = 262\%
2
What is the time in this equation for a a continuously declining bacteria population?
A LaTex expression showing 633 =700 times e to the power of (-0.02 times 5)
a A LaTex expression showing t = 5
b A LaTex expression showing t = 633
c A LaTex expression showing t = 700
3
What is the time in this equation for a continuous decline of a whale population?
A LaTex expression showing 753 =800 times e to the power of (-0.03 times 2)
a A LaTex expression showing t = 753
b A LaTex expression showing t = 2
c A LaTex expression showing t = 800
4
What is the rate in this equation for a continuous reduction of a toxin concentration?
A LaTex expression showing 708 =900 times e to the power of (-0.04 times 6)
a A LaTex expression showing r = 900\%
b A LaTex expression showing r = 707\%
c A LaTex expression showing r = 4\%
5
What is the final concentration in this equation for a continuous reduction of a toxin concentration?
A LaTex expression showing 277 =300 times e to the power of (-0.04 times 2)
a A LaTex expression showing C = 300
b A LaTex expression showing C = 277
c A LaTex expression showing C = 4
6
What is the starting concentration in this equation for a continuous reduction of a toxin concentration?
A LaTex expression showing 256 =300 times e to the power of (-0.02 times 8)
a A LaTex expression showing C sub 0 = 255
b A LaTex expression showing C sub 0 = 300
c A LaTex expression showing C sub 0 = 8
7
What is the starting population in this equation for a continuous decline of a whale population?
A LaTex expression showing 466 =800 times e to the power of (-0.09 times 6)
a A LaTex expression showing P sub 0 = 6
b A LaTex expression showing P sub 0 = 800
c A LaTex expression showing P sub 0 = 466
8
What is the rate in this equation for a a continuously declining bacteria population?
A LaTex expression showing 305 =400 times e to the power of (-0.09 times 3)
a A LaTex expression showing r = 305\%
b A LaTex expression showing r = 9\%
c A LaTex expression showing r = 400\%