Question

Statistics indicate that the world population sinceworld war II has been growing exponentially. If weassume exponential growth, the world population canbe modeled by P (t) = 6(1.025)^t where P(t) isthe world population in billions and t is the time inyears since 1995.When (which year) will the population reach 12 billion?{your final answer just number without decimal}

Answer 1

P(t) = 6 ( 1.025 ) ^t

Let p(t) = 12 since the equation is given in billions

12 = 6 ( 1.025 ) ^t

Divide each side by 6

12/6 = 6/6 ( 1.025 ) ^t

2 = ( 1.025 ) ^t

Now take the natural log of each side

ln(2) = ln( ( 1.025 ) ^t)

Using the exponent rule ln( a^b) = b ln a

ln (2) = t ln ( 1.025)

Divide each side by ln(1.025)

ln (2) / ln(1.025) = t

28.01703= t

Rounding to the nearest year

28 years from the start

The start was 1995

1995+28 = 2023

The year would be 2023