The answer is 16.
<h2>Step-by-step explanation:</h2>Since the 8x is positive, the equation must have y as a positive number.
Let's see this!
An easy way to complete the square if you have the constants for x2 and
But not the non-variable number is to divide the x constant, and then square it.
Example:
The last number must be 16. Let's check it.
Answer:
Step-by-step explanation:
The logistic equation is the following one:
In which P(t) is the size of the population after t years, K is the carrying capacity of the population, r is the decimal growth rate of the population and P(0) is the initial population of the lake.
In this problem, we have that:
Biologists stocked a lake with 80 fish and estimated the carrying capacity (the maximal population for the fish of that species in that lake) to be 2,000. This means that .
The number of fish tripled in the first year. This means that .
Using the equation for P(1), that is, P(t) when , we find the value of r.
Applying ln to both sides.
This means that the expression for the size of the population after t years is: