## 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: Limited Growth Differential Equation

– WHEN A PRODUCT IS ADVERTISED HEAVILY SALES WILL TEND TO GROW VERY QUICKLY BUT EVENTUALLY THE MARKET WILL REACH SATURATION AND THE SALES WILL SLOW. THIS TYPE OF GROWTH IS CALLED LIMITED GROWTH. FOR THE LIMITED GROWTH DIFFERENTIAL EQUATION IF A QUANTITY GROWS AT A RATE PROPORTIONAL TO THE DISTANCE FROM THE MAXIMUM VALUE M IT CAN […]

## Ex: Logistic Growth Differential Equation

– IF A QUANTITY GROWS AT A RATE PROPORTIONAL TO IT’S SIZE AND TO THE DISTANCE FROM THE MAXIMUM VALUE M IT CAN BE MODELED WITH LOGISTIC GROWTH USING THE DIFFERENTIAL EQUATION Y PRIME=R x Y x THE QUANTITY 1 – Y DIVIDED BY M WHERE WHY IS THE GROWTH RATE ABSENT CONSTRAINTS AND M IS THE MAXIMUM […]

## Exponential Growth: Recursive and Explicit Equations Part 1

– WELCOME TO PART ONE OF A LESSON ON EXPONENTIAL GROWTH. IN THIS LESSON WE’LL EXPRESS EXPONENTIAL GROWTH IN RECURSIVE FORM AS WELL AS EXPLICIT FORM. SUPPOSE THERE ARE 4,000 STUDENTS ATTENDING A LOCAL COMMUNITY COLLEGE AND THE NUMBER OF STUDENTS IS INCREASING BY 5% EACH YEAR. HOW MANY STUDENTS WILL ATTEND THE COLLEGE IN FOUR YEARS? SUPPOSE […]

## 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 […]

## Ex: Find an Recursive and Explicit Equation for Exponential Growth Given r

– STARTING IN THE YEAR 2012, THE NUMBER OF SPEEDING TICKETS ISSUED EACH YEAR IN P TOWN IS PREDICTED TO GROW ACCORDING TO AN EXPONENTIAL GROWTH MODEL. DURING THE YEAR 2012, WHICH IS THE STARTING YEAR, P TOWN ISSUED 190 SPEEDING TICKETS AND THEREFORE P SUB 0=190. THIS ALSO TELLS US N=0, CORRESPONDS TO THE YEAR 2012. NEXT, […]