C\) atoms remaining in the scull after \(t\) years of radioactive decay. Since \(^{14}C\) has a half life of 5700 years we have \(f(0)=1\) and \(f(5700)=0.5\text{.}\) Sketch the graph of \(f(t ...

All sorts of microorganisms exhibit patterns that are very close to exponential population growth. For example, in the right hand graph of Figure 2 is a population of Paramecium growing in a ...

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 ...

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.

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 ...