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suppose the population of a small town is 19000 and growing exponentially at 2.3%. how many years until the population until the population reaches 26000

Respuesta :

opudodennis

Answer:

14 years

Step-by-step explanation:

Using the general growth formula

[tex]F=P(1+r/100)^{n}[/tex] 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

[tex]26000=19000(1+2.3/100)^{n}[/tex]

[tex](1+0.023)^{n}=\frac {26000}{19000}[/tex]

[tex]1.023^{n}=\frac {26000}{19000}[/tex]

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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