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Answer:
[tex]t > 5[/tex]
Step-by-step explanation:
Given
[tex]a = 15[/tex] ---- Initial
[tex]r = 3[/tex] --- rate
Required
The inequality that represents people more than 3000
The given parameters show a geometric sequence and will be calculated using:
[tex]T_t = ar^{t-1[/tex]
Where t is the number of days
For the people to be more than 3000, the expression becomes:
[tex]ar^{t-1} > 3000[/tex]
Substitute values for a and r
[tex]15 * 3^{t-1} > 3000[/tex]
Divide both sides by 15
[tex]3^{t-1} > 200[/tex]
Take log of both sides
[tex]Log3^{t-1} > Log200[/tex]
Apply law of logarithm
[tex](t-1)Log3 > Log200[/tex]
Make t - 1 the subject
[tex]t - 1 > \frac{Log200}{Log3}[/tex]
[tex]t - 1 > 4.82[/tex]
Add 1 to both sides
[tex]t - 1 +1> 4.82 +1[/tex]
[tex]t > 5.82[/tex]
Round down
[tex]t > 5[/tex]