EXPONENTIAL FUNCTIONS PRE-CALCULUS UNIT 3. EXPONENTIAL GROWTH WHEN HAVE YOU SEEN EXPONENTIAL GROWTH...
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Transcript of EXPONENTIAL FUNCTIONS PRE-CALCULUS UNIT 3. EXPONENTIAL GROWTH WHEN HAVE YOU SEEN EXPONENTIAL GROWTH...
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EXPONENTIAL FUNCTIONS
PRE-CALCULUS UNIT 3
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EXPONENTIAL GROWTH
•WHEN HAVE YOU SEEN EXPONENTIAL GROWTH IN A REAL-WORLD SITUATION?
•WHAT ARE SOME PROPERTIES OF EXPONENTIAL GROWTH FUNCTIONS?
•DOMAIN/RANGE, INTERCEPTS, CONTINUITY, END BEHAVIOR, ETC.
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EXPONENTIAL DECAY•WHEN HAVE YOU SEEN EXPONENTIAL DECAY IN A REAL-WORLD SITUATION?
•WHAT ARE SOME PROPERTIES OF EXPONENTIAL DECAY FUNCTIONS?
•DOMAIN/RANGE, INTERCEPTS, CONTINUITY, END BEHAVIOR, ETC.
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EXPONENTIAL GROWTH AND DECAY•EXPONENTIAL GROWTH AND DECAY FORMULA:
•WHERE N˳ IS THE INITIAL AMOUNT
•R IS THE GROWTH RATE IF R > 0
•R IS THE DECAY RATE IF R < 0
•T IS THE AMOUNT OF TIME
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EXPONENTIAL GROWTH AND DECAY•CONTINUOUS EXPONENTIAL GROWTH AND DECAY FORMULA:
•WHERE N˳ IS THE INITIAL AMOUNT
•K IS THE CONTINUOUS GROWTH RATE, THEN K > 0
•K IS THE CONTINUOUS DECAY RATE, THEN K < 0
•T IS THE AMOUNT OF TIME
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GROWTH OR DECAY
•MEXICO HAS A POPULATION OF APPROXIMATELY 110 MILLION PEOPLE. IF MEXICO’ S POPULATION CONTINUES TO GROW AT THE DESCRIBED RATE, PREDICT THE POPULATION OF MEXICO IN 10 AND 20 YEARS.
• IF GROWTH RATE IS 1.42% ANNUALLY
• IF GROWTH RATE IS 1.42% CONTINUOUSLY
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GROWTH OR DECAY
•THE POPULATION OF A TOWN IS DECLINING AT A RATE OF 6%. IF THE CURRENT POPULATION IS 12,426 PEOPLE, PREDICT THE POPULATION IN 5 AND 10 YEARS USING:
•ANNUALLY
•CONTINUOUSLY
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EXAMPLES
•JASMINE RECEIVES A 3.5% RAISE AT THE END OF EACH YEAR FROM HER EMPLOYER TO ACCOUNT FOR INFLATION. WHEN SHE STARTED WORKING FOR THE COMPANY IN 1994, SHE WAS EARNING A SALARY OF $31,000.
•WHAT WAS JASMINES SALARY IN 2000? 2009?
•WHAT WILL IT BE IN 2024?
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EXAMPLES
•THE HALF-LIFE OF A RADIOACTIVE SUBSTANCE IS THE AMOUNT OF TIME IT TAKES FOR HALF OF THE ATOMS OF THE SUBSTANCE TO DISINTEGRATE. URANIUM-235 IS USED TO FUEL A COMMERCIAL POWER PLANT. ITS HALF-LIFE IS 704 MILLION YEARS.
•HOW MANY GRAMS OF URANIUM WILL REMAIN AFTER 1 MILLION YEARS IF YOU START WITH 200 GRAMS?
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EXAMPLES
•UNDER THE RIGHT GROWING CONDITIONS A PARTICULAR SPECIES OF PLANT HAS A DOUBLING TIME OF 12 DAYS. SUPPOSE A PASTURE CONTAINS 46 PLANTS OF THIS SPECIES. HOW MANY PLANTS WILL THEIR BE AFTER 20, 65, AND X DAYS?
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TRUE OR FALSE
•EXPONENTIAL FUNCTIONS CAN NEVER HAVE RESTRICTIONS ON THE DOMAIN.
•EXPONENTIAL FUNCTIONS ALWAYS HAVE RESTRICTIONS ON THE RANGE
•GRAPHS OF EXPONENTIAL FUNCTIONS ALWAYS HAVE AN ASYMPTOTE.
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EXTRA PRACTICE
•WORKSHEET
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M&M ACTIVITY
•FOLLOW THE DIRECTIONS ON THE WORKSHEET.
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COMPOUND INTEREST
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COMPOUND INTEREST
•FORMULA:
• •WHERE P = INITIAL AMOUNT INVESTED, R = INTEREST RATE, T = TIME
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COMPOUND INTEREST
•CONTINUOUS COMPOUND FORMULA:
•USED ONLY WHEN DOING COMPOUNDED DAILY!
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COMPOUND INTEREST•WHAT ARE THE DIFFERENT TYPES OF COMPOUNDING?
•ANNUALLY
•SEMI-ANNUALLY
•QUARTERLY
•MONTHLY
•WEEKLY
•DAILY
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COMPOUND INTEREST
•IF I INVESTED $500 INTO AN ACCOUNT WHICH YIELDS 5% ANNUAL INTEREST, HOW MUCH WOULD I HAVE AFTER 7 YEARS IF THE INTEREST WAS COMPOUNDED
•ANNUALLY
•QUARTERLY
•DAILY
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COMPOUND INTEREST
•KRYSTI INVESTS $1200 IN AN ACCOUNT WITH A 6% INTEREST RATE, MAKING NO OTHER DEPOSITS OR WITHDRAWLS. WHAT WILL KRYSIT’S ACCOUNT BALANCE BE AFTER 20 YEARS IF THE INTEREST IS COMPOUNDED:
•SEMI-ANNUALLY
•MONTHLY
•DAILY
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COMPOUND INTEREST
•WHICH SHOULD I INVEST $1200 IN?
•A 3 YEAR CD WITH 3.45% INTEREST COMPOUNDED CONTINUOUSLY
•A 5 YEAR CD WITH 4.75% INTEREST COMPOUNDED MONTHLY?