In a previous blog, I described how the half life of a particle can be used to solve exponential decay problems. In this blog, I will use logarithms to describe…

Sometimes, there are tricky questions such as the following: $$ \lim_{x \to 3} \frac{x \; - \, 3}{\sqrt{x^2 \; - \, 9}} $$ Both the numerator and the denominator tend…

How do you calculate the sum of an infinite number of things? Normally, that is impossible. However, if the infinite sum is a geometric series, it can be done. First,…

In calculus, people are interested in calculating limits such as the following: $$ \lim_{x \to \infty} \frac{3x^3 + 5}{2x^3 \; - \; 1,000,000\,x^2} $$ To calculate this, we need to…

The half-life of a substance is the amount of time it takes for that substance to deplete by 50 percent. A typical problem goes as follows: The half-life of uranium…