Exponential Growth

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sweetliljenny

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Nov 5, 2006
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1. Statistics indicate that the world population since World War II has been growing continuously at the rate of 1.9% per year. United Nations records indicate that the world population in 1975 was (approx.) 4 billion. Assuming an exponential growth model:

a. What was the population of the world in the year 2000? (Use 2 decimal places)
b. To the nearest yet, when will the world population be 10 billion?
c. What was the population of the world back in 1946, just after the end of WWII? (Use 2 decimal places)
 
P = 4(1.019)<sup>t</sup>
where P = population in billions and t = time in years where 1975 is t = 0.

now that you have the hard part done (the equation), here are some hints ...

(a) the year 2000 is t = 25

(b) 10 = 4(1.019)<sup>t</sup> ... solve for t

(c) if 1975 is t = 0, what is t in 1946?
 
i got part a

P = 4(1.019) ^ 25 = 6.40 billion

however with part b i'm a little confused
10 = 4(1.019) ^ t

divide 4 by both sides which equals
2.5 = 1.019 ^ t

i need help after that part though
 
i did part c ... 1975 - 1946 = 29
therefore t = -29

P = 4(1.019) ^ -29 = approx. 2.32 billion


and yes i've done logs before
but i don't recall doing anything like
1.109 ^ t = 2.5 ---> log 1.019 ^ t = log 2.5
 
log(2.5) = log(1.019<sup>t</sup>)

log(2.5) = t*log(1.019)

log(2.5)/log(1.019) = t
 
thank u so much
luckily before i got to ur post too i had found the rule that

ln A ^ c = c x ln A


you've been a doll ..thank you for all the help =)
 
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