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:
<span>8d – 4d – 6d – 8 = 2d
</span><span>8d – 4d – 6d – 2d = 8
-4d = 8
d = -2</span>
Answer:
31/100
Step-by-step explanation:
To turn .31 into a fraction we need to multiply it by 100
.31*100=31.
Now we need to divide it by 100
31/100
Since 31 is prime we can not simplify it.
I think the three box.sorry if wrong
Answer:
We can define a horizontal dilation/contraction of scale factor A, as:
g(x) = f(x*A)
if A > 1, this will be a contraction (it will be steeper)
if 0 < A < 1, this will be a dilation. (it will be less steep)
Then if we have:
g(x) = f(6*x) we have a contraction of scale factor 6, this means that the graph of the parent function will be contracted.
Below, you can see how the graphs change, where:
Blue is f(x) =x
green is g(x) = f(6*x) = 6*x
