Question

The equation y=6.72(1.014) x models the world population y , in billions of people, x years after the year 2000 . Find the year in which the world population is about 8 billion.

Answer 1

the population will reach 8 billion by 2012 ,as calculated by properties of logarithm.

What is Logarithm?

• The opposite of exponentiation is the logarithm.
• This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.
• A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.

Given:

• y = 6.72 ( $1.014^x$), where

1. y = population in billions
2. x = time in years

To find: Year when population is 8 billion, i.e., y = 8.

Finding:

8 = 6.72  ( $1.014^x$)

=> $\frac{8}{6.72}= ( 1.014^x)$

Taking log on both sides

=> $log(\frac{8}{6.72})= log( 1.014^x)$

=> log(1.19) = x (log 1.014) (as $log_b(a)^m = m (log_b(a))$ )

=> $\frac{log(1.19)}{log (1.014)}$ = x

=> x = $\frac{0.0755}{0.006}$

=> x = 12.58

Hence, the population will reach 8 billion by 2012 ,as calculated by properties of logarithm.

To learn more about logarithms, refer to the link: brainly.com/question/25710806

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