Question

The number of people who like a particular video online triples every day after the day the video is posted. If 15 people like the video on the day it is posted, which inequality can be used to find the number of days, t , it takes for the number of people who have liked the video to reach more than 3,000?

Answer 1

`t > 5`

Explanation:

Given

`a = 15` ---- Initial

`r = 3` --- rate

Required

The inequality that represents people more than 3000

The given parameters show a geometric sequence and will be calculated using:

`T_t = ar^{t-1`

Where t is the number of days

For the people to be more than 3000, the expression becomes:

`ar^(t-1) > 3000`

Substitute values for a and r

`15 * 3^(t-1) > 3000`

Divide both sides by 15

`3^(t-1) > 200`

Take log of both sides

`Log3^(t-1) > Log200`

Apply law of logarithm

`(t-1)Log3 > Log200`

Make t - 1 the subject

`t - 1 > (Log200)/(Log3)`

`t - 1 > 4.82`

Add 1 to both sides

`t - 1 +1> 4.82 +1`

`t > 5.82`

Round down

`t > 5`