Question

in a hypothetical human population of 1000 individuals showing exponential growth every female gives birth to 0.3 children per year. death rate is 0.1 per capita per year. what will be the population size after 10 years (e=2.72).

1)7389 2)1500 3)3699 4)1649

Answer 1

${\huge{\underline{\underline{\bold{\purple{Answer:-}}}}}}$

➡ No = population size in 1993 = 5.4 billion

➡ t = 7 years (year 2000 - 1993)

➡ r = 0.0139 (from question above)

➡ Nt = No e^rt

➡ Nt = (540,000,000) e^ (0.0139)(7)

➡ Nt /540,000,000 = e^ 0.0973

Dust off your high school math skills. To get rid of the exponent, simply take the natural log (ln) of both sides of the equation. Remember, when we take the natural log of a quotient we end up taking the ln of one value and subtracting it from the ln of the other value (see below).

ln (Nt /540,000,000) = ln (e^ 0.0973)

[here we're taking the natural log of the quotient]

➡ = ln(Nt) - ln(540,000,000) = 0.0973

[rewrite it as natural log of one value minus natural log of the other value]

➡ Nt = 595,000,000 or 5.95 billion!

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$\huge{\boxed{Thanks:-)}}$