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Exponential Function Solving - Decay (Discrete) Equation to Value at Time

Level 1

The math topic primarily focuses on solving exponential decay problems in various scenarios using discrete functions. It involves calculating the final values over time, based on initial conditions, decay rates, and time periods. The problems are set in contexts such as the financial balance of endowments, the concentration of toxins during dialysis, and the size of whale populations during breeding cycles. Each question provides an exponential decay function and asks to determine the correct final value from multiple choices, enhancing understanding of exponential decay models applied practically.

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

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Exponential Function Solving - Decay (Discrete) Equation to Value at Time Worksheet

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Exponential Function Solving - Decay (Discrete) Equation to Value at ...
1
Solve for the final cash given this model of a balance of a charitable endowment (weekly disbursements)?
A LaTex expression showing P =300 times (1-0.04) to the power of (5)
a A LaTex expression showing P = P sub 0 times (1 - r) to the power of ( t)
b A LaTex expression showing 1 + P = P sub 0 over (1 - r) to the power of ( t)
c A LaTex expression showing 0 + P = P sub 0 times (1 + r) to the power of ( t)
d A LaTex expression showing 6 + P = P sub 0 over (1 - r) to the power of ( t)
2
Solve for the final concentration given this model of a decline of a toxin concentration (daily dialysis)?
A LaTex expression showing C =300 times (1-0.07) to the power of (9)
a A LaTex expression showing 3 + C = C sub 0 times (1 + r) to the power of ( t)
b A LaTex expression showing C = C sub 0 times (1 - r) to the power of ( t)
c A LaTex expression showing 4 + C = C sub 0 times (1 + r) to the power of ( t)
d A LaTex expression showing 6 + C = C sub 0 over (1 - r) to the power of ( t)
3
Solve for the final population given this model of a decline of a whale population (yearly breeding cycle)?
A LaTex expression showing P =800 times (1-0.04) to the power of (5)
a A LaTex expression showing P = P sub 0 times (1 - r) to the power of ( t)
b A LaTex expression showing 7 + P = P sub 0 times (1 + r) to the power of ( t)
c A LaTex expression showing 2 + P = P sub 0 times (1 + r) to the power of ( t)
d A LaTex expression showing 8 + P = P sub 0 times (1 + r) to the power of ( t)
4
Solve for the final concentration given this model of a decline of a toxin concentration (hourly dialysis)?
A LaTex expression showing C =800 times (1-0.05) to the power of (9)
a A LaTex expression showing C = C sub 0 times (1 - r) to the power of ( t)
b A LaTex expression showing 8 + C = C sub 0 times (1 + r) to the power of ( t)
c A LaTex expression showing 9 + C = C sub 0 over (1 - r) to the power of ( t)
d A LaTex expression showing 3 + C = C sub 0 over (1 - r) to the power of ( t)
5
Solve for the final population given this model of a decline of a whale population (yearly breeding cycle)?
A LaTex expression showing P =400 times (1-0.09) to the power of (2)
a A LaTex expression showing P = P sub 0 times (1 - r) to the power of ( t)
b A LaTex expression showing 6 + P = P sub 0 times (1 + r) to the power of ( t)
c A LaTex expression showing 2 + P = P sub 0 times (1 + r) to the power of ( t)
d A LaTex expression showing 3 + P = P sub 0 over (1 - r) to the power of ( t)
6
Solve for the final concentration given this model of a decline of a toxin concentration (daily dialysis)?
A LaTex expression showing C =800 times (1-0.02) to the power of (9)
a A LaTex expression showing 2 + C = C sub 0 times (1 + r) to the power of ( t)
b A LaTex expression showing C = C sub 0 times (1 - r) to the power of ( t)
c A LaTex expression showing 0 + C = C sub 0 times (1 + r) to the power of ( t)
d A LaTex expression showing 1 + C = C sub 0 over (1 - r) to the power of ( t)
7
Solve for the final concentration given this model of a decline of a toxin concentration (hourly dialysis)?
A LaTex expression showing C =700 times (1-0.02) to the power of (8)
a A LaTex expression showing 7 + C = C sub 0 over (1 - r) to the power of ( t)
b A LaTex expression showing C = C sub 0 times (1 - r) to the power of ( t)
c A LaTex expression showing 4 + C = C sub 0 times (1 + r) to the power of ( t)
d A LaTex expression showing 1 + C = C sub 0 times (1 + r) to the power of ( t)
8
Solve for the final concentration given this model of a decline of a toxin concentration (hourly dialysis)?
A LaTex expression showing C =200 times (1-0.08) to the power of (5)
a A LaTex expression showing 1 + C = C sub 0 over (1 - r) to the power of ( t)
b A LaTex expression showing C = C sub 0 times (1 - r) to the power of ( t)
c A LaTex expression showing 2 + C = C sub 0 over (1 - r) to the power of ( t)
d A LaTex expression showing 7 + C = C sub 0 times (1 + r) to the power of ( t)