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The population (in millions) of a certain country can be approximated by the function; P(x)=100•1.02^x where x is the number of years after 2000. which of the following calculations will tell in what year the population can be expected to reach 300 million?

A. In(3)/In(1.02)
B. In(3/1.02)
C. In(3/1.02)+2000
D. In(3)/In(1.02) +2000

Options are shown in image.

The population in millions of a certain country can be approximated by the function Px100102x where x is the number of years after 2000 which of the following c class=

Respuesta :

Option A

[tex]x = \frac{ln\ 3}{ln\ 1.02}[/tex]

Solution:

Given that,

The population (in millions) of a certain country can be approximated by the function:

[tex]P(x) = 100 (1.02)^x[/tex]

In what year the population can be expected to reach 300 million?

Therefore,

P(x) = 300 million

[tex]300 = 100(1.02)^x\\\\\frac{300}{100} = 1.02^x\\\\1.02^x = 3[/tex]

Take ln on both sides

[tex]x\ ln\ 1.02 = ln\ 3\\\\Therefore\\\\x = \frac{ln\ 3}{ln\ 1.02}[/tex]

Thus option A is correct

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