Question

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?

Answer 1

a)
`x = \log_(2) 9,000,000`, b)
`x \approx 23.101\,days`

Explanation:

The number of readers as a function of time is:

`n = 2^(x)`

Where:

`x` - Time, measured in days.

`n` - Number of readers, dimensionless.

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

`x = \log_(2) n`

`x = \log_(2) 9,000,000`

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

`x \approx 23.101\,days`