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

Level 1

This math topic involves solving exponential decay problems related to concentrations of toxins and population sizes. Each question presents a scenario where a toxin or population starts at a specified concentration or size and decreases weekly or yearly by a given percentage. Over a certain period, the final concentration or population size must be calculated using an exponential decay formula. The exponential function primarily takes the form \( C = C_0 \times (1 - r)^t \), where \(C_0\) is the initial concentration or size, \(r\) is the decay rate, and \(t\) is the time elapsed.

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

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

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Exponential Function Solving - Decay (Discrete) Scenario to Value at ...
1
A toxin starts at a concentration of 400mg/L. Each weekly dialysis reduces it by 5%. After 6 weeks it has decreased to a certain concentration.
Solve for the final concentration given this scenario?
a A LaTex expression showing C = C sub 0 times (1 - r) to the power of ( t)
b A LaTex expression showing 4 + C = C sub 0 times (1 + r) to the power of ( t)
c A LaTex expression showing 8 + C = C sub 0 over (1 - r) to the power of ( t)
d A LaTex expression showing 9 + C = C sub 0 over (1 - r) to the power of ( t)
2
A toxin starts at a concentration of 300mg/L. Each weekly dialysis reduces it by 6%. After 4 weeks it has decreased to a certain concentration.
Solve for the final concentration given this scenario?
a A LaTex expression showing C = C sub 0 times (1 - r) to the power of ( t)
b A LaTex expression showing 6 + C = C sub 0 times (1 + r) to the power of ( t)
c A LaTex expression showing 3 + C = C sub 0 times (1 + r) to the power of ( t)
d A LaTex expression showing 5 + C = C sub 0 over (1 - r) to the power of ( t)
3
A toxin starts at a concentration of 900mg/L. Each weekly dialysis reduces it by 7%. After 4 weeks it has decreased to a certain concentration.
Solve for the final concentration given this scenario?
a A LaTex expression showing 9 + C = C sub 0 times (1 + r) to the power of ( t)
b A LaTex expression showing 6 + C = C sub 0 over (1 - r) to the power of ( t)
c A LaTex expression showing 1 + C = C sub 0 over (1 - r) to the power of ( t)
d A LaTex expression showing C = C sub 0 times (1 - r) to the power of ( t)
4
A bird population starts at 900. Each subsequent year it declines by 7%. After 8 years it has decreased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing 9 + P = P sub 0 over (1 - r) to the power of ( t)
b A LaTex expression showing P = P sub 0 times (1 - r) to the power of ( t)
c A LaTex expression showing 7 + P = P sub 0 over (1 - r) to the power of ( t)
d A LaTex expression showing 7 + P = P sub 0 times (1 + r) to the power of ( t)
5
A whale population starts at 300. Each subsequent year it declines by 6%. After 8 years it has decreased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing 3 + P = P sub 0 times (1 + r) to the power of ( t)
b A LaTex expression showing P = P sub 0 times (1 - r) to the power of ( t)
c A LaTex expression showing 7 + P = P sub 0 over (1 - r) to the power of ( t)
d A LaTex expression showing 6 + P = P sub 0 times (1 + r) to the power of ( t)
6
A whale population starts at 400. Each subsequent year it declines by 5%. After 3 years it has decreased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing P = P sub 0 times (1 - r) to the power of ( t)
b A LaTex expression showing 0 + P = P sub 0 over (1 - r) to the power of ( t)
c A LaTex expression showing 7 + P = P sub 0 over (1 - r) to the power of ( t)
d A LaTex expression showing 4 + P = P sub 0 over (1 - r) to the power of ( t)
7
A whale population starts at 700. Each subsequent year it declines by 5%. After 4 years it has decreased to a certain population.
Solve for the final population given this scenario?
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 4 + P = P sub 0 times (1 + r) to the power of ( t)
d A LaTex expression showing 4 + P = P sub 0 over (1 - r) to the power of ( t)
8
A toxin starts at a concentration of 300mg/L. Each daily dialysis reduces it by 4%. After 8 days it has decreased to a certain concentration.
Solve for the final concentration given this scenario?
a A LaTex expression showing C = C sub 0 times (1 - r) to the power of ( t)
b A LaTex expression showing 1 + C = C sub 0 over (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)