
Explore how e relates to exponential growth, analyze it with the binomial theorem and factorial series, and relate luck to solving real exponential problems like carbon dating.
Explore the meaning of e by modeling growth as a limit of discrete steps approaching continuous growth, using unit growth and binomial theorem to analyze how end values approach e.
Learn to decompose a complex growth expression into expandable components using the binomial theorem. See how coefficients reflect the number of ways to choose periods for growth.
Explore how to compute binomial coefficients by counting selections and removing order effects, introduce factorial notation, and present the binomial theorem and its expansion for any positive integers.
Compute e through an infinite factorial series derived from a binomial theorem, illustrating continuous growth and compound interest as the limit approaches 2.71828.
Learn how the number e expresses natural change across growth and decay, with e^r for positive rates and e^-r for decay, including rational and continuous compounding.
Discover how continuous growth uses e to the power of a growth rate and learn to infer the log rate from observed outcomes like doubling or tripling a unit.
Compute log as the growth rate needed for one unit to reach X, using incremental steps and mother-cell contributions, with e-based validation and a weighted-series approach.
Explore how the relationship between e and log solves exponential problems by converting bases to e and using natural logs to find x, as in 2^x = 50.
Explore how exponential change links status and time using e and log, then apply carbon dating to estimate age from carbon-14 decay and log-based ratios.
Are you currently studying log and e and find the concepts confusing? Are you seeking better resources to help you understand the topics? Are you curious about the real life application? Or are you familiar with applications of e and log but want to gain a solid understanding about them? Then this course is for you! It’s a spinoff from our bigger project of learning math through stock price modeling. The repeated occurrences of e and log in real life applications remind us that understanding them will be crucial in understanding most modern techniques. So we decide to make it a separate course to help anyone who are struggling with the subjects. Our course offers the best explanations on e and log.
It clearly explains what e means, how to analyze it, and how to compute it. It also explains what log means and how to compute any log by hand! Then it talks about the relationship between e and log and how to use that relationship to solve real world problems!
We are confident that our content is the best because we understand why most materials are failing: because several different concepts are mixed together. That’s why when we developed this course, we focused on peeling the topics into the basic components. This way, we can explain each component clearly and later on the intertwining relationships can be illustrated easily.