High School

A culture of bacteria has an initial population of 94,000 bacteria and doubles every 10 hours. Using the formula

\[ P(t) = P_0 \cdot 2^{\frac{t}{d}} \]

where \( P(t) \) is the population after \( t \) hours, \( P_0 \) is the initial population, \( t \) is the time in hours, and \( d \) is the doubling time, what is the population of bacteria in the culture after 13 hours, to the nearest whole number?

Answer :

The population is modeled by the exponential equation:

P(x) = 94,000*(2)^(x/10)

And the population after 13 hours is 231,455 bacteria.

What is the population after 13 hours?

The population can be modeled with an exponential equation of the form:

P(x) = A*(b)^x

Where A is the initial population, b defines the rate of growth/decay, and x represents the time.

Here the initial population is 94,000 bacteria, and it doubles every 10 hours, then we can write the exponential equation as:

P(x) = 94,000*(2)^(x/10)

Notice that there is a 1/10 factor in the exponent because the doubling thing happens every 10 hours, then the population after 13 hours is:

P(13) =94,000*(2)^(13/10) = 231,455 bacteria.

Learn more about exponential equations at:

https://brainly.com/question/11832081

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