SOLUTION: *GLOBAL POPULATION (P) INCREASED EXPONENTIALLY AT A RATE OF 1.8% PER ANNUM FROM 1950 TO 1980. GLOBAL FOOD PRODUCTION (F)INCREASED LINEARLY DURING THE SAME PERIOD FROM 370 billion k

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Question 108374: *GLOBAL POPULATION (P) INCREASED EXPONENTIALLY AT A RATE OF 1.8% PER ANNUM FROM 1950 TO 1980. GLOBAL FOOD PRODUCTION (F)INCREASED LINEARLY DURING THE SAME PERIOD FROM 370 billion kg to 1650 billion kg. THE GLOBAL POPULATION IN 1950 WAS 2.6 BILLION(2,556,518,868)HUMANS.
WHAT IS THE EQUATION THAT PREDICTS THE POPULATION OVER THIS PERIOD AS A FUNCTION OF TIME, ALSO WRITE THE EQUATION THAT SHOWS FOOD PRODUCTION OVER THIS PERIOD OF TIME.
USE YOUR EQUATION TO FIND THE POPULATION AND THE FOOD PRODUCTION IN 1976.
WHAT WOULD BE THE POPULATION IN 2007?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Exponential function
N%28t%29=N%5B0%5De%5E%28kt%29
k=0.018%2Fyear
N%5B0%5D=2556518868
a.)N%28t%29=2556518868e%5E%280.018t%29
Linear function
b.) F%28t%29=mt%2Bb
m+=+%28F%5B2%5D-F%5B1%5D%29%2F%28t%5B2%5D-t%5B1%5D%29
m+=+%281650-350%29%2F%281980-1950%29
m+=+1300%2F30
m+=+130%2F3
Pick one of your values to determine b
1650=%28130%2F3%29%281980%29%2Bb
b=84150
F%28t%29=%28130%2F3%29t-84150
where t is the year and F(t) is billions kg.
c.)t=1976-1950=26
N%28t%29=2556518868e%5E%280.018%2826%29%29
N%28t%29=2556518868e%5E%280.468%29%29
N%28t%29=2556518868%281.5967974%29%29
N%28t%29=4082242688
N(1976) = 4.1 billion (4,082,242,688) humans
F%28t%29=%28130%2F3%29t-84150
F%281976%29=%28130%2F3%291976-84150
F%281976%29=%28130%2F3%291976-84150
F%281976%29=85627-84150
F%281976%29=1477
F(1976)=1477 billion kg
d.) Assuming the exponential population model is still valid,
t=2007-1950=57
N%28t%29=2556518868e%5E%280.018%2857%29%29
N%28t%29=2556518868e%5E%281.026%29
N%28t%29=2556518868%282.789884%29
N%28t%29=7132390958
N(2007) = 7.1 billion (7,132,390,958) humans