Answer:
(c)
Step-by-step explanation:
Given
See attachment for A and B
Required
Compare A and B
First, we get the initial population of A and B.
The initial population is at when
From the table of bacteria A, we have:
when
From the graph of bacteria B, we have:
when
Since the initial of bacteria B is less than that of bacteria A, then (a) is incorrect.
Next, calculate the slope of A and B i.e. the rate
Slope (m) is calculated as:
Where
y = Number of bacteria
t = time
For bacteria A:
So, the slope is:
For bacteria B:
So, the slope is:
Since , then the rate of bacteria B is greater than that of bacteria A.
<em>Hence, (d) cannot be true</em>
Next, we determine the equation of both bacteria
This is calculated using:
For bacteria A, we have:
Where:
So:
For bacteria B, we have:
Where:
So:
At 3 hours, the population of bacteria A is:
At 3 hours, the population of bacteria B is:
After 3 hours, bacteria B is 150 while A is 160.
This implies that (c) is correct because the population of B is less than that of A, at 3 hour
Lastly, to check if they will ever have equal population or not, we simply equate both equations.
So, we have:
Collect like terms
Solve for t
They will have equal population at 5 hours.
Hence, b is incorrect
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<em>From the above computation, only (c) is correct</em>
