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

Level 1

This math topic focuses on solving continuous decay exponential function scenarios to find the value of a population or concentration at a specific time. It includes problems where bacterial populations or isotopic concentrations start with an initial amount and decrease continuously over time at a given percentage rate. Students are required to apply the exponential decay formula to solve for the final population or concentration values after the specified years, weeks, months, or days have passed. Each problem provides multiple-choice solutions involving exponential expressions, enhancing understanding of exponential decay 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 Solving - Decay (Continuous) Scenario to Value at Time Worksheet

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Exponential Function Solving - Decay (Continuous) Scenario to Value a...
1
A bacteria population starts at 900. It declines continuously at 8% per year. After 6 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 e to the power of (-r times t)
b A LaTex expression showing 1 + P = P sub 0 times e to the power of (-r over t )
c A LaTex expression showing 9 + P = P sub 0 times e to the power of (-r over t )
d A LaTex expression showing 6 + P = P sub 0 - e to the power of (-r times t)
2
A bacteria population starts at 500. It declines continuously at 2% per week. After 7 weeks it has decreased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing 2 + P = P sub 0 - e to the power of (-r times t)
b A LaTex expression showing P = P sub 0 times e to the power of (-r times t)
c A LaTex expression showing 0 + P = P sub 0 - e to the power of (-r times t)
d A LaTex expression showing 4 + P = P sub 0 times e to the power of (-r over t )
3
A bacteria population starts at 900. It declines continuously at 6% per month. After 3 months it has decreased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing 8 + P = P sub 0 - e to the power of (-r times t)
b A LaTex expression showing 7 + P = P sub 0 - e to the power of (-r times t)
c A LaTex expression showing P = P sub 0 times e to the power of (-r times t)
4
A bacteria population starts at 600. It declines continuously at 2% per month. After 8 months it has decreased to a certain population.
Solve for the final population given this scenario?
a A LaTex expression showing 4 + P = P sub 0 times e to the power of (-r over t )
b A LaTex expression showing 5 + P = P sub 0 times e to the power of (-r over t )
c A LaTex expression showing 0 + P = P sub 0 - e to the power of (-r times t)
d A LaTex expression showing P = P sub 0 times e to the power of (-r times t)
5
A radioactive material starts at an isotope concentration of 500ppm. It decays continuously at 4% per day. After 6 days it has decayed to a certain isotope concentration.
Solve for the final concentration given this scenario?
a A LaTex expression showing R = R sub 0 times e to the power of (-r times t)
b A LaTex expression showing 4 + R = R sub 0 times e to the power of (-r over t )
c A LaTex expression showing 9 + R = R sub 0 - e to the power of (-r times t)
d A LaTex expression showing 8 + R = R sub 0 times e to the power of (-r over t )
6
A whale population starts at 600. It declines continuously at 9% per year. After 5 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 e to the power of (-r over t )
b A LaTex expression showing 6 + P = P sub 0 times e to the power of (-r over t )
c A LaTex expression showing P = P sub 0 times e to the power of (-r times t)
d A LaTex expression showing 1 + P = P sub 0 - e to the power of (-r times t)
7
A bird population starts at 800. It declines continuously at 7% per quarter. After 2 quarters 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 - e to the power of (-r times t)
b A LaTex expression showing 2 + P = P sub 0 - e to the power of (-r times t)
c A LaTex expression showing P = P sub 0 times e to the power of (-r times t)
d A LaTex expression showing 6 + P = P sub 0 times e to the power of (-r over t )
8
A whale population starts at 200. It declines continuously at 3% per year. After 8 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 e to the power of (-r times t)
b A LaTex expression showing 5 + P = P sub 0 - e to the power of (-r times t)
c A LaTex expression showing 7 + P = P sub 0 - e to the power of (-r times t)