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In the context of growth and decay, what does the differential equation $\frac{dN}{dt} = kN$ represent?
In the context of growth and decay, what does the differential equation $\frac{dN}{dt} = kN$ represent?
What is the original amount of bacteria in a culture if it is known to grow at a rate proportional to the amount present, and after 1 hour there are 1000 strands, and after 4 hours there are 3000 strands?
What is the original amount of bacteria in a culture if it is known to grow at a rate proportional to the amount present, and after 1 hour there are 1000 strands, and after 4 hours there are 3000 strands?
What is the half-life of a substance if its decay can be modeled by the equation $N(t) = N_0e^{-kt}$?
What is the half-life of a substance if its decay can be modeled by the equation $N(t) = N_0e^{-kt}$?
If a radioactive substance decays from 800 grams to 100 grams in 30 days, what is the decay constant $k$ in the equation $N(t) = N_0e^{-kt}$?
If a radioactive substance decays from 800 grams to 100 grams in 30 days, what is the decay constant $k$ in the equation $N(t) = N_0e^{-kt}$?
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What does a negative value of the constant of proportionality $k$ signify in the context of growth and decay?
What does a negative value of the constant of proportionality $k$ signify in the context of growth and decay?
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