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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?
- Linear growth
- Linear decay
- Exponential decay
- Exponential growth (correct)
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?
- 5000 strands
- 693.3641 strands (correct)
- 1200 strands
- 800 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 $N(t) = N_0e^{-kt}$?
- $\frac{k}{2}$
- $\frac{k}{0.693}$
- $\frac{1}{k}$
- $\frac{0.693}{k}$ (correct)
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 $N(t) = N_0e^{-kt}$?
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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