suppose the population of a small town is 19000 and growing exponentially at 2.3%. how many years until the population until the
1 answer:
Answer:
14 years
Step-by-step explanation:
Using the general growth formula
where F is future population, P is present population, n is years and r is rate in percentage.
Substituting 26000 for future population F, 19000 for present population P and 2.3% for rate
Introducing natural logarithms on both sides
n ln 1.023=ln(\frac {26000}{19000})[/tex]
n=(ln 26/19)/(ln 1.023)=13.79351958 years
Rounding off, n=14 years
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Step-by-step explanation:
We can model the annual consumption of iron by the equation
c = 900 million tons x , where
n is the number of years after 1993 and
c is the consumption for that year.
An estimate for the total consumption of iron can now be obtained by integrating this equation with respect to a dummy variable, x from 0 to n.
This equation simplifies to
C = 900 million tons x (1.025^n - 1) / ln(1.025), where
x is a dummy variable and
C is the total consumption of iron n years after 1993.
Let R be the amount of iron remaining at n years after 1993, so
R = 480 billion tons - C
R = 480 billion tons - 900 million tons x (1.025^n - 1) / ln(1.025)
We need to find the value of n when R is 0, so
0 = 480 billion tons - 900 million tons x (1.025^n - 1) / ln(1.025)
Simplify this equation to obtain
n = 107.4
So the iron will run out in the year 1993 + 107 = 2100