If the world's population was 6 billion in 2000 and grows at a rate of 2%, in what year is it projected to reach 12 billion?

To determine when the world's population will reach 12 billion, starting from a base of 6 billion in the year 2000 and growing at a constant rate of 2% per year, we can employ the formula for exponential growth, which is:

[ P = P_0(1 + r)^t ]

Where:

• ( P ) is the future population,

• ( P_0 ) is the initial population (6 billion),

• ( r ) is the growth rate (0.02), and

• ( t ) is the number of years since the initial population was measured.

We want to find the value of ( t ) when the population ( P ) reaches 12 billion. Plugging the values into the formula gives us:

[ 12 = 6(1 + 0.02)^t ]

Simplifying this:

[ 2 = (1.02)^t ]

To solve for ( t ), we take the logarithm of both sides:

[ \log(2) = t \cdot \log(1.02) ]

Now, by rearranging the equation, we can calculate ( t ):

[ t = \frac{\log(