If the per capita growth rate of the world population continues to be what it was in the year 2000, the world population t years after July 1, 2000, will be 6.085 × 1.0121^t billion. According to this formula, when will the world population reach 9 billion? A)41.3 years after July 1, 2000 B)32.5 years after July 1, 2000 C)22.7 years after July 1, 2000 D)6.8 years after July 1, 2000

Question

Quizplus · Accepted Answer

We are given the formula:

World population (in billions) = 6.085 × 1.0121^t

We need to find out when the world population will reach 9 billion, so we can set up the following equation:

9 = 6.085 × 1.0121^t

Divide both sides by 6.085:

1.476 = 1.0121^t

Take the natural logarithm of both sides:

ln(1.476) = ln(1.0121^t)

Using the property of logarithms that ln(a^b) = b ln(a), we can simplify the right side:

ln(1.476) = t ln(1.0121)

Finally, solve for t by dividing both sides by ln(1.0121):

t = ln(1.476) / ln(1.0121) ≈ 32.5

Therefore, the world population will reach 9 billion about 32.5 years after July 1, 2000. 
The answer is B.

If the Per Capita Growth Rate of the World Population