# What Does B^(2t/C) Represent in Bacterial Growth Modeling?

• Niaboc67
It should be P(t) = Ae^(kt), where A = 1200 and k = 0.0231. B and C are not necessary to solve for this equation. B represents the initial amount of bacteria, which is already given as 1200, and C represents the doubling time, which is 30 minutes. In summary, the function that models the number of bacteria after t minutes is P(t) = 1200e^(0.0231t).
Niaboc67
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A culture contains 1200 bacteria initially and doubles every 30 minutes. Assuming that the rate of growth is proportional to the number of bacteria, find a function that models the number P(t) of bacteria after t minutes.

P(t) = A e^(kt) = B^(2t/C)
, where A = 1200
k = 0.0231
B = ?
C = ?

I was able to figure out A and K fine. But where does B and C mean?

Thank you

Niaboc67 said:
A culture contains 1200 bacteria initially and doubles every 30 minutes. Assuming that the rate of growth is proportional to the number of bacteria, find a function that models the number P(t) of bacteria after t minutes.

P(t) = A e^(kt) = B^(2t/C)
Are you sure you copied the equation correctly?

## 1. What is the meaning of B^(2t/C)?

The expression B^(2t/C) represents the value of B raised to the power of 2t divided by C. It is a mathematical notation used to denote exponential functions.

## 2. How do you solve for B in B^(2t/C)?

To solve for B in B^(2t/C), we can take the Cth root of both sides of the equation. This means that B = (B^(2t/C))^(1/C), or B = (B^2t)^(1/C), which simplifies to B = B^(2t/C).

## 3. What does the variable t represent in B^(2t/C)?

In this expression, t represents a variable or number that is being multiplied by 2 and then divided by C. It is commonly used in mathematical equations to represent a changing or unknown quantity.

## 4. How is B^(2t/C) related to exponential growth and decay?

B^(2t/C) is a common form of the exponential growth and decay equation, where B represents the initial value, t represents time, and C represents the rate of change. This expression is used to model processes that grow or decay at a constant rate over time.

## 5. Can B^(2t/C) be negative?

Yes, B^(2t/C) can be negative. The value of B will determine whether the expression is positive or negative. When B is negative, the result will be negative regardless of the values of t and C. When B is positive, the result may be positive or negative depending on the values of t and C.

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