Answer:
19 days
Step-by-step explanation:
Given
[tex]a = 150[/tex] --- initial
[tex]r = 8\%[/tex] -- rate
Required
Days when the fish gets to 30
The function is exponential and as such it follows;
[tex]y = ab^x[/tex]
Where x represents the number of days and y the number of fishes
Because the fishes decreases;
[tex]b = 1 - r[/tex]
So, we have:
[tex]b = 1 - 8\%[/tex]
Express as decimal
[tex]b = 1 - 0.08[/tex]
[tex]b = 0.92[/tex]
In [tex]y = ab^x[/tex]
[tex]a =150[/tex]
[tex]y = 30[/tex]
[tex]b = 0.92[/tex]
So, we have:
[tex]30 = 150 * 0.92^x[/tex]
Divide both sides by 150
[tex]0.2 = 0.92^x[/tex]
Take log of both sides
[tex]log(0.2) = log(0.92^x)[/tex]
Apply law of logarithm
[tex]log(0.2) = x\ log(0.92)[/tex]
Make x the subject
[tex]x = \frac{log(0.2)}{log(0.92)}[/tex]
[tex]x = \frac{-0.6990}{-0.0362}[/tex]
[tex]x = 19.309[/tex]
[tex]x \approx 19[/tex]
Hence, it takes approximately 19 days
