September 28, 2019 0

Ex: Exponential Growth Application – Predicting World Population

Ex: Exponential Growth Application – Predicting World Population


– THE WORLD POPULATION
WAS 4.8 BILLION IN 1985, WITH AN ESTIMATED GROWTH RATE
OF 1.8% PER YEAR. ASSUMING THE WORLD POPULATION
FOLLOWS THIS EXPONENTIAL GROWTH MODEL, FIND THE PROJECTED POPULATION
IN 2020 ROUND TO TWO DECIMAL PLACES. SO TO SOLVE THIS PROBLEM WE’LL USE THE EXPONENTIAL
FUNCTION GIVEN HERE, P OF T=P SUB 0 x E
RAISED TO THE POWER OF K x T. WHERE P OF T WOULD BE THE
POPULATION AFTER T YEARS. P SUB 0 WOULD BE THE STARTING
OR INITIAL POPULATION. K WOULD BE THE ANNUAL GROWTH
RATE EXPRESSED AS A DECIMAL, AND T WOULD BE THE TIME
IN YEARS. SO LOOKING AT THE GIVEN
INFORMATION, THE STARTING POPULATION
WOULD BE 4.8 BILLION, SO P SUB 0=4.8 BILLION. THE ANNUAL GROWTH RATE IS 1.8%, SO R=1.8%, WHICH MUST BE
EXPRESSED AS A DECIMAL, WHICH WOULD BE 0.018. AND WE’RE ASKED TO FIND THE
POPULATION IN THE YEAR 2020, WHERE THE GIVEN INFORMATION
IS FROM 1985. SO T WOULD BE THE NUMBER
OF YEARS AFTER 1985, WHICH WOULD BE 2020 – 1985,
WHICH IS EQUAL TO 35. SO WE WANT TO FIND P OF 35. SO OUR FUNCTION IS GOING TO BE P
OF T=P SUB 0 OR 4.8 x E RAISED TO THE POWER OF K x T,
WHICH WOULD BE 0.018 x T. BUT NOW WE ALSO KNOW THAT T IS
EQUAL TO 35 FOR THE YEAR 2020. SO WE WANT TO FIND P OF 35, WHICH IS EQUAL TO 4.8 x E RAISED
TO THE POWER OF 0.018 x 35. AND NOW WE’LL GO
TO THE CALCULATOR. WE HAVE 4.8. IF WE PRESS SECOND NATURAL LOG THAT BRINGS UP E RAISED
TO THE POWER OF, AND THEN WE HAVE 0.018 x 35. AND WE’RE ASKED TO ROUND
TO TWO DECIMAL PLACES, WHICH WOULD BE APPROXIMATELY
9.01. SO THE PROJECTED POPULATION
IN 2020 IS 9.01 BILLION. I HOPE YOU FOUND THIS HELPFUL.  

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