Growth of bacteria

Definition

The growth of bacteria typically follows an exponential pattern, which can be modeled using exponential functions. In calculus, this concept is crucial for solving integrals involving exponential growth and decay.

5 Must Know Facts For Your Next Test

1. Bacterial growth can be represented by the function $N(t) = N_0 e^{kt}$, where $N_0$ is the initial quantity, $k$ is the growth rate, and $t$ is time.
2. The integral of an exponential function such as $e^{kt}$ is essential for determining the total bacterial population over a given time period.
3. Logarithmic functions are used to solve for time or rates when dealing with exponential bacterial growth equations.
4. The natural logarithm $\ln(x)$ is often used in solving integrals that involve bacterial growth due to its relationship with the base $e$.
5. In problems involving bacterial growth, you may need to apply techniques such as integration by parts or substitution to solve more complex integrals.

Review Questions

• What function typically models the exponential growth of bacteria?
• How do you integrate an exponential function like $e^{kt}$ when calculating total population over time?
• When solving for time in a bacterial growth model, what logarithmic function might you use?

Related terms

Exponential Function: A mathematical function of the form $f(x) = a e^{bx}$ where $a$ and $b$ are constants and $e$ is Euler's number.

Natural Logarithm: The logarithm to the base $e$, written as $\ln(x)$, which is used to solve equations involving exponential growth.

Integration by Parts: A technique used to integrate products of functions based on the formula $\int u dv = uv - \int v du$.