# Geometric Sequence Problems

Growth and decay problems involve repeated multiplications by a constant number, a common ratio. We can thus use geometric sequences to model these situations. \large \begin{align} \require{AMSsymbols} \displaystyle\require{color} \color{red}u_{n} &= u_{1} \times r^{n-1} \\\require{color} \color{red}u_{n+1} &= u_{1} \times r^{n}\end{align} Example 1 The initial population of chickens on a farm was $40$. The population increased […]

# Exponential Growth and Decay using Logarithms

It has been known how exponential functions can be used to model various growth and decay situations. These included the growth of populations and the decay of radioactive substances. This lesson considers more growth and decay problems, focusing on how logarithms can be used in their solution. Population Growth Example 1 The area $A_{t}$ affected […]

# Logarithm Definition

A logarithm determines “$\textit{How many of this number do we multiply to get the number?}$”. The exponent gives the power to which a base is raised to make a given number.For example, $5^2=25$ indicates that the logarithm of $25$ to the base $5$ is $2$.$$\large 25=5^2 \Leftrightarrow 2=\log_{5}{25}$$If $b=a^x,a \ne 1, a>0$, we say […]