An internet story that goes viral has a number of readers that is increasing exponentially, with number of readers in millions represented by 2x, where x is the time, in days. Find the time when the number of readers reaches 9 million.

What is the exact solution written as a logarithm?

What is an approximate solution rounded to the nearest thousandth?

Respuesta :

Answer:

a) [tex]x = \log_{2} 9,000,000[/tex], b) [tex]x \approx 23.101\,days[/tex]

Step-by-step explanation:

The number of readers as a function of time is:

[tex]n = 2^{x}[/tex]

Where:

[tex]x[/tex] - Time, measured in days.

[tex]n[/tex] - Number of readers, dimensionless.

a) The time when the number of readers reaches 9 million is:

[tex]x = \log_{2} n[/tex]

[tex]x = \log_{2} 9,000,000[/tex]

b) The approximate solution rounded to the nearest thousandth is:

[tex]x \approx 23.101\,days[/tex]