Question

A pond has 150 fish and the population decreases by 8% each day. How many days before there are 30 fish

Answer 1

Answer:

19 days

Step-by-step explanation:

Given

$a = 150$ --- initial

$r = 8\%$ -- rate

Required

Days when the fish gets to 30

The function is exponential and as such it follows;

$y = ab^x$

Where x represents the number of days and y the number of fishes

Because the fishes decreases;

$b = 1 - r$

So, we have:

$b = 1 - 8\%$

Express as decimal

$b = 1 - 0.08$

$b = 0.92$

In $y = ab^x$

$a =150$

$y = 30$

$b = 0.92$

So, we have:

$30 = 150 * 0.92^x$

Divide both sides by 150

$0.2 = 0.92^x$

Take log of both sides

$log(0.2) = log(0.92^x)$

Apply law of logarithm

$log(0.2) = x\ log(0.92)$

Make x the subject

$x = \frac{log(0.2)}{log(0.92)}$

$x = \frac{-0.6990}{-0.0362}$

$x = 19.309$

$x \approx 19$

Hence, it takes approximately 19 days