## Ex: Find the Initial Value and Exponential Growth or Decay Rate Given an Exponential Function

– IN THIS PROBLEM WE’RE GIVEN SIX EXPONENTIAL FUNCTIONS. THREE OF THEM ARE EXPONENTIAL GROWTH AND THREE OF THEM ARE EXPONENTIAL DECAY. FOR EACH FUNCTION WE WANT TO FIND THE INITIAL VALUE AND ALSO THE GROWTH OR DECAY RATE AS A PERCENTAGE. TO BEGIN, LETS IDENTIFY WHICH FUNCTIONS ARE EXPONENTIAL GROWTH, AND WHICH ARE EXPONENTIAL DECAY. FOR EXPONENTIAL […]

## Ex: Exponential Growth of Bacteria (Intro Question)

– THE NUMBER OF BACTERIA IN A CULTURE IS N OF T AFTER T HOURS. SO THE FUNCTION THAT MODELS THE NUMBER OF BACTERIA, OR THE BACTERIA POPULATION, IS N OF T=500 x E RAISED TO THE POWER OF 0.15T. WHEN WE HAVE EXPONENTIAL GROWTH, WE CAN GATHER A LOT OF INFORMATION FROM THE EXPONENTIAL GROWTH FUNCTION. IN […]

## Logistic Growth: Using Recursive Equations

– WELCOME TO A LESSON ON LOGISTIC GROWTH USING RECURSIVE FORMULAS. IN THIS LESSON WE’LL DERIVE A RECURSIVE LOGISTIC GROWTH EQUATION AND ALSO FIND POPULATION LEVELS USING LOGISTIC GROWTH. IN OUR BASIC EXPONENTIAL GROWTH SCENARIO WE HAD A RECURSIVE EQUATION IN THE FORM P SUB N=P SUB N – 1 + R, THE GROWTH RATE EXPRESSED AS A […]

## Ex: Find an Exponential Growth Function Given Two Points – Initial Value Given

– IN THIS QUESTION WE’RE ASKED TO DETERMINE AN EXPONENTIAL FUNCTION THAT PASSES THROUGH THE POINTS (0, 15) AND (5, 480). WE ALSO WANT TO KNOW WHAT THE EXPONENTIAL GROWTH OR DECAY RATE IS. WE ALSO WANT TO FIND THE FUNCTION VALUE WHEN X=2. IF AN EXPONENTIAL FUNCTION IS IN THIS FORM HERE THEN THE BASE B IS […]

## The Psychology of Solitude: Being Alone Can Maximize Productivity, with Scott Barry Kaufman

A lot of people fear solitude yet the great psychiatrist Winnicott said that the capacity for solitude is one of the greatest markers of psychological health. So if you can develop your capacity for solitude that means that you are okay being alone with yourself. As Cal Newport who wrote the book Deep Work notes some of the […]