Complete Question
The model that describes the number of bacteria in a culture after t days has just been updated from [tex]P(t) = 7(2)^t[/tex] to [tex]P(t) = 7(3)^t[/tex] What implications can you draw from this information?
A The growth rate of the bacteria in the culture is 30% per day instead of
20% per day.
B The final number of bacteria is 3 times as much of the initial value instead
of 2 times as much.
C The initial number of bacteria is 3 instead of 2
D The number of bacteria triples every day instead of doubling every day
E None of the above.
Answer:
The correct option is D
Step-by-step explanation:
From the question we are told that
The first model is [tex]P(t) = 7(2)^t[/tex]
The updated model is [tex]P(t) = 7(3)^t[/tex]
Generally looking the two models that define the number of bacteria we see that at the for the first model that the number is being doubled everyday for example if the time is equal to 1 day we have that
[tex]P(1) = 7(2)^1[/tex]
[tex]P(1) = 2 * 7[/tex]
Here we see that the constant 7 is being double but in the new model we can see that the number is being triple everyday , taking the same example with t = 1
[tex]P(1) = 7(3)^1[/tex]
=> [tex]P(1) = 3 * 7 [/tex]
Here we see that the constant 7 is being triple for each day
Hence the implication of the model change is that the number of bacteria will be tripled everyday instead of being doubled everyday
