Scientists released 5 foxes into a new habitat in year 0. Each year, there were
1 answer:
Answer:
Step-by-step explanation:
Since every year there are four times as many foxes as the year before, every year we need to multiply the previous population by 4. This leads to having to multiply by after n years have gone by. So we are in the presence of a population growth that goes as an exponential function of base "4".
A function f(x) that represents an exponential growth of such type can be written as:
where x represents the variable time in years, 4 is the multiplicative base, and is what is defined as the "initial value" of the population (in our case 5 - for the 5 foxes initially released).
Notice also that when we start counting - time zero (x=0) the exponential form becomes a one (1) and the expression reduces to this initial value
(5 in our case).
Therefore, the function representing this population growth is:
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Answer: The intersection region shown in the graph attached is the solution of the system of inequalities.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
Where "m" is the slope and "b" is the y-intercept.
Given the following system of inequalities:
We need to graph the lines.
We have the line:
Solving for "y", we get:
Knowing that and
, we can graph it.
Since the symbol is , the line must be solid.
The other line is:
Since "x" only takes one value, we can identify that it is a vertical line, so we can graph it.
Since the symbol is , the line must be solid.
We need to substitute a point that is not on the line, into each inequalities. Let's choose the point (0,0).
Then:
This is false, therefore, we must shade the half that does not contain this point.
This is false, so we must shade the half that does not contain this point.
The intersection region of the solutions (Observe the graph attached) of the given inequalities is the solution of the system of inequalities.
