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

Level 1

This math topic focuses on solving exponential decay equations in a continuous setting to determine population values at specific times. It includes multiple problems where students are tasked with calculating the future population of birds or bacteria. The process involves using an initial population value and applying an exponential decay formula that factors in a decay rate and a time period. Students select an appropriate mathematical expression that models the scenario provided. This topic falls under an introductory unit on exponential functions and emphasizes understanding and applying continuous decay models 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) Equation to Value at Time Worksheet

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Exponential Function Solving - Decay (Continuous) Equation to Value a...
1
Solve for the final population given this model of a continuous decline of a bird population?
A LaTex expression showing P =900 times e to the power of (-0.04 times 5)
a A LaTex expression showing 4 + P = P sub 0 - e to the power of (-r times t)
b A LaTex expression showing 4 + 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)
2
Solve for the final population given this model of a continuous decline of a bird population?
A LaTex expression showing P =300 times e to the power of (-0.05 times 8)
a A LaTex expression showing 1 + P = P sub 0 - e to the power of (-r times 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 P = P sub 0 times e to the power of (-r times t)
3
Solve for the final population given this model of a continuous decline of a bird population?
A LaTex expression showing P =300 times e to the power of (-0.04 times 9)
a A LaTex expression showing P = P sub 0 times e to the power of (-r times t)
b A LaTex expression showing 0 + P = P sub 0 times e to the power of (-r over t )
c A LaTex expression showing 7 + P = P sub 0 times e to the power of (-r over t )
d A LaTex expression showing 9 + P = P sub 0 times e to the power of (-r over t )
4
Solve for the final population given this model of a a continuously declining bacteria population?
A LaTex expression showing P =600 times e to the power of (-0.08 times 2)
a A LaTex expression showing 6 + P = P sub 0 times e to the power of (-r over t )
b A LaTex expression showing 3 + P = P sub 0 - e to the power of (-r times t)
c A LaTex expression showing 8 + 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
Solve for the final population given this model of a continuous decline of a bird population?
A LaTex expression showing P =200 times e to the power of (-0.04 times 3)
a A LaTex expression showing 8 + P = P sub 0 - e to the power of (-r times t)
b A LaTex expression showing 0 + 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)
6
Solve for the final population given this model of a a continuously declining bacteria population?
A LaTex expression showing P =900 times e to the power of (-0.02 times 7)
a A LaTex expression showing 9 + 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)
d A LaTex expression showing 8 + P = P sub 0 - e to the power of (-r times t)
7
Solve for the final population given this model of a a continuously declining bacteria population?
A LaTex expression showing P =800 times e to the power of (-0.05 times 9)
a A LaTex expression showing 0 + P = P sub 0 - e to the power of (-r times 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 6 + 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)
8
Solve for the final population given this model of a continuous decline of a bird population?
A LaTex expression showing P =300 times e to the power of (-0.04 times 8)
a A LaTex expression showing P = P sub 0 times e to the power of (-r times t)
b A LaTex expression showing 8 + P = P sub 0 times e to the power of (-r over t )
c A LaTex expression showing 5 + P = P sub 0 - e to the power of (-r times t)
d A LaTex expression showing 0 + P = P sub 0 - e to the power of (-r times t)