EXPONENTIAL FUNCTIONS

PRE-CALCULUS UNIT 3

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.

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.

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

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

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

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

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?

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?

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?

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.

EXTRA PRACTICE

•WORKSHEET

M&M ACTIVITY

•FOLLOW THE DIRECTIONS ON THE WORKSHEET.

COMPOUND INTEREST

COMPOUND INTEREST

•FORMULA:

• •WHERE P = INITIAL AMOUNT INVESTED, R = INTEREST RATE, T = TIME

COMPOUND INTEREST

•CONTINUOUS COMPOUND FORMULA:

•USED ONLY WHEN DOING COMPOUNDED DAILY!

COMPOUND INTEREST•WHAT ARE THE DIFFERENT TYPES OF COMPOUNDING?

•ANNUALLY

•SEMI-ANNUALLY

•QUARTERLY

•MONTHLY

•WEEKLY

•DAILY

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

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

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?