obeys the decay differential equation: \begin{equation ... the number of bacteria increased tenfold in 10 hours. Assuming natural growth, how long did it take for their number to double? A bacterial ...

The pattern of growth is very close to the pattern of the exponential equation. which is kind of remarkable, because it says that the rate of growth of the log of the number in the population is ...

Definite and indefinite integrals and the Fundamental Theorem of Calculus. Simple differential equations (separable ODE, linear ODE). ODE models leading to exponential growth and decay.

Data from an experiment may result in a graph indicating exponential growth. This implies the formula of this growth is \(y = k{x^n}\), where \(k\) and \(n\) are constants. Using logarithms ...

Recall that the solution of the initial-value problem \(y^\prime=ky\text{,}\) \(y(0)=A\text{,}\) is given by \(\ds y=Ae^{kx}\text{.}\) Solve the following problems ...