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10 6 Exponential Growth and Decay Worksheet Answer Key  Form

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- 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 MODEL THIS SITUATION, WHERE P SUB 0 IS A STARTING POPULATION, K IS THE EXPONENTIAL GROWTH RATE, T IS THE TIME IN HOURS, AND P OF T WOULD BE THE POPULATION AFTER T HOURS. WE FIRST WANT TO EXPRESS THE POPULATION AFTER T HOURS AS A FUNCTION OF T. THEN WE WANT TO FIND THE POPULATION AFTER SIX HOURS. THEN WE WANT TO KNOW WHEN THE POPULATION WILL REACH 5,000. SO LETS START BY FINDING THE EXPONENTIAL FUNCTION THAT WILL MODEL THE BACTERIA POPULATION. WE'RE STARTING WITH 200 BACTERIA, WHICH MEANS P SUB 0 = 200 AND THEN AFTER THREE HOURS THERE WILL BE 900 BACTERIA. SO WHEN T = 3 THE POPULATION, OR P OF T, IS GOING TO BE EQUAL TO 900. WE'RE GOING TO SUB THESE VALUES INTO OUR EXP

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