Question

How do I set up modelling equations for problems?

For example
Exponential growth. If the growth rate of the number of bacteria at any time t is proportional to the number present at t and doubles in 1 week, how many bacteria can be expected after 2 weeks? After 4 weeks?

Answer 1

let x be the number of bacteria. The growth rate is the change in x over time \( \frac{dx}{dt}\)
growth rate proportional to the number present means
\[ \frac{dx}{dt} = k \cdot x \]
where k is the constant of proportionality