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Courtney L.

asked • 09/08/18

EXPONENTIAL EQUATIONS & FUNCTIONS

EXPONENTIAL EQUATIONS & FUNCTIONS
1)A culture of bacteria doubles in weight approximately every 2.5 hours. The number of bacteria after t hours later can be approximated by 𝑁(𝑡) = 175(2.5)𝑡
a) How many bacteria would there be initially (𝑡 = 0)?

2)Solve for x.
a) 43−2𝑥 = 64 b) 25𝑥+1 = 53𝑥
b) Find 𝑁(4). What does this number tell you in terms of this problem?
 
 

Arturo O.

If t is the number of hours, the given equation for N(t) is not correct.  Assuming that 175 is the initial weight of the bacteria, N(t) should be
 
N(t) = 175 (2)t/2.5
 
The equation must have 2 raised to the power equal to the number of doubling periods, which is the elapsed time t divided by the duration of a doubling period of 2.5 hours.
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09/08/18

Courtney L.

??(??) = 175(2.5)t        
 
This is what the paper says for my homework Im just not understanding this problem 
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09/09/18

Arturo O.

That equation is not consistent with the information provided in the problem statement.  That equation states that the weight increases by a factor of 2.5 every hour, which is not the same doubling every 2.5 hours.  Starting with an initial weight of 175, the equation that is consistent with the wording of the problem is
 
N(t) = 175 (2)t/2.5
 
with t in hours.
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09/09/18

1 Expert Answer

By:

Jeffrey K. answered • 09/27/20

Tutor
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