Please help vey simple math problem
2 answers:
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Answer:
a)
b)
Step-by-step explanation:
For this case we have the following info:
represent the initial amount of bacteria
represent the population of bacteria after 6 hours
Part a
For this case we use the proportional model given by:
Where P represent the population at time t and k is a constant of proportionality.
We can rewrite the model like this:
And if we integrate both sides we got:
Now if we apply exponential we got:
For this case using the initial condition:
We have the following model:
Using the second condition we have this:
We can divide both sides by 660 and we got:
Now we can apply natural log on both sides and we got:
So then the model would be given by:
Part b
For this case we just need to replace t=3 into the model and we got:
Answer:
A. Yes, (0,0) satisfies both inequalities.
Step-by-step explanation:
The given inequalities are;
and
For (0,0) to be a solution to the given system of inequalities then it must satisfy both inequalities.
We substitute (0,0) into the system of inequalities to obtain;
This implies that;
; True
and
This implies that;
: True
Since (0,0) satisfies the two systems, it is a solution.
The correct choice is A.