# Tag: equation

## 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 Function – Population

– A GROWING CITY HAD A POPULATION OF 500,000 IN 2005, IN 2010 THE POPULATION WAS 760,000. WE WANT TO ASSUME EXPONENTIAL GROWTH AND THEN EXPRESS THE POPULATION AFTER T YEARS AS A FUNCTION OF T, PREDICT THE POPULATION IN 2025, AND THEN DETERMINE IN WHICH YEAR THE POPULATION WILL REACH 1,000,000. SO WE WANT TO START BY […]

## Separable Differential Equations & Growth and Decay Model Calculus 1 AB

BAM!! Mr. Tarrou. In this lesson, we are going to use our newfound skills of solving separable differential equations and apply those to growth and decay models. We will do 4 examples, first one working with variables that are inversely proportional to each other. The second example is going to be a direct application of the rules and […]

## Ex: Inverse Variation Application – Number of Workers and Job Time

– THE TIME, T, REQUIRED TO DO A JOB VARIES INVERSELY WITH THE NUMBER OF PEOPLE, P, WORKING ON THE JOB. IF IT TAKES SIX HOURS FOR EIGHT WORKERS TO COMPLETE A JOB, HOW LONG WOULD IT TAKE IF THERE WERE NINE WORKERS? SO, SOMETIMES WHEN WE HAVE AN INVERSE VARIATION APPLICATION LIKE THIS, IT’S A LITTLE MORE […]

## 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: Exponential Growth Function – Bacterial Growth

– A BACTERIA CULTURE STARTING WITH 200 BACTERIA GROWS AT A RATE PROPORTIONAL TO ITS SIZE. AFTER THREE HOURS, THERE WILL BE 900 BACTERIA. THIS IS AN EXAMPLE OF AN EXPONENTIAL GROWTH. THIS IS AN EXPONENTIAL GROWTH MODEL. SO WE’LL BE USING THE FUNCTION P OF T=P SUB 0 x E RAISED TO THE POWER OF KT TO […]

## 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, […]