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the initial number of bacteria in a culture is 12,000. the xulture doubles each day write an exponential functin to model the population Y of bacteria after X days

  • MsEHolt: The equation would be y=12000(2)ˣ.

    This equation is of the form y=a*bˣ, where a is the initial population and b is the rate that it increases by.  In this problem, a = 12000 and b=2, since it doubles each time.
  • OrethaWilkison:

    Answer:

    [tex]Y = 12,000 \cdot (2)^X[/tex]

    Step-by-step explanation:

    The exponential function is given by:

    [tex]y =a \cdot b^x[/tex]

    where,

    a is the initial values and b is the growth factor.

    As per the statement:

    The initial number of bacteria in a culture is 12,000.

    ⇒Number of bacteria initially(a) = 12,000

    It is also given that the culture doubles each day.

    ⇒ growth factor [tex]b= 2[/tex]

    We have to find the exponential function to model the population Y of bacteria after X days.

    By definition of exponential function:

    [tex]Y = 12,000 \cdot (2)^X[/tex]

    where, x represents the days and Y is the population after X days.

    Therefore,  an exponential function to model the population is,

    [tex]Y = 12,000 \cdot (2)^X[/tex]

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