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Exponential Function Decay (Discrete) - Meaning to Term

Level 1

This math topic focuses on understanding and identifying components of the exponential decay function \( P = P_0 \times (1-r)^t \) in various contexts. Each problem requires identifying a specific term in the formula (such as the starting population, final cash, rate of decline, or time) given a scenario like wildlife population decline, charitable endowment balance, or concentration of a toxin. It helps students connect abstract mathematical concepts with real-world applications, fostering critical thinking about how exponential decay functions operate over time.

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

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Exponential Function Decay (Discrete) - Meaning to Term Worksheet

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Exponential Function Decay (Discrete) - Meaning to Term
1
In this model of decline of a whale population (yearly breeding cycle), which term represents the starting population?
A LaTex expression showing P =P sub 0 times (1 - r) to the power of (t) \\\text{starting population} = ?
a A LaTex expression showing r
b A LaTex expression showing P
c A LaTex expression showing P sub 0
d A LaTex expression showing t
2
In this model of balance of a charitable endowment (yearly disbursements), which term represents the final cash?
A LaTex expression showing P =P sub 0 times (1 - r) to the power of (t) \\\text{final cash} = ?
a A LaTex expression showing P
b A LaTex expression showing t
c A LaTex expression showing r
3
In this model of decline of a bird population (yearly breeding cycle), which term represents the rate?
A LaTex expression showing P =P sub 0 times (1 - r) to the power of (t) \\\text{rate} = ?
a A LaTex expression showing r
b A LaTex expression showing P
c A LaTex expression showing P sub 0
d A LaTex expression showing t
4
In this model of decline of a bird population (yearly breeding cycle), which term represents the time?
A LaTex expression showing P =P sub 0 times (1 - r) to the power of (t) \\\text{time} = ?
a A LaTex expression showing t
b A LaTex expression showing P sub 0
c A LaTex expression showing P
5
In this model of decline of a whale population (yearly breeding cycle), which term represents the final population?
A LaTex expression showing P =P sub 0 times (1 - r) to the power of (t) \\\text{final population} = ?
a A LaTex expression showing r
b A LaTex expression showing t
c A LaTex expression showing P
6
In this model of decline of a toxin concentration (monthly dialysis), which term represents the starting concentration?
A LaTex expression showing C =C sub 0 times (1 - r) to the power of (t) \\\text{starting concentration} = ?
a A LaTex expression showing C
b A LaTex expression showing r
c A LaTex expression showing C sub 0
d A LaTex expression showing t
7
In this model of balance of a charitable endowment (weekly disbursements), which term represents the starting cash?
A LaTex expression showing P =P sub 0 times (1 - r) to the power of (t) \\\text{starting cash} = ?
a A LaTex expression showing t
b A LaTex expression showing P sub 0
c A LaTex expression showing r
d A LaTex expression showing P
8
In this model of decline of a toxin concentration (hourly dialysis), which term represents the time?
A LaTex expression showing C =C sub 0 times (1 - r) to the power of (t) \\\text{time} = ?
a A LaTex expression showing C
b A LaTex expression showing C sub 0
c A LaTex expression showing t