After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly. The population loses (1)/(4) of its size every 44 seconds. The number of remaining bacteria can be modeled by a function, N, which depends on the amount of time, t (in seconds). Before the medicine was introduced, there were 11,880 bacteria in the Petri dish. Write a function that models the number of remaining bacteria t seconds since the medicine was introduced. N(t)=◻

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After a special medicine is introduced into a petri dish containing a bacterial culture, the number of bacteria remaining in the dish decreases rapidly. The population loses  (1)/(4) of its size every 44 seconds. The number of remaining bacteria can be modeled by a function,  N, which depends on the amount of time,  t (in seconds). Before the medicine was introduced, there were 11,880 bacteria in the Petri dish. Write a function that models the number of remaining bacteria  t seconds since the medicine was introduced.  N(t)=◻

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Identify initial amount and rate: Identify the initial amount of bacteria and the rate of decrease. The initial amount of bacteria (a) is given as 11,880. The bacteria population decreases by 1/4 of its size every 44 seconds, which means the remaining fraction of the population after each decrease is 3/4 (since 1 - 1/4 = 3/4).Determine decay factor: Determine the decay factor (b). The decay factor (b) is the fraction of the population that remains after each time interval. In this case, every 44 seconds, the population retains 3/4 of its size. Therefore, b = 3/4.Write exponential decay function: Write the exponential decay function. The general form of an exponential decay function is N(t) = a(b)^t, where N(t) is the number of bacteria at time t, a is the initial amount, b is the decay factor, and t is the time in the same units as the decay interval. However, since the decay happens every 44 seconds, we need to adjust the exponent to reflect the number of 44-second intervals that have passed. This means we divide t by 44 to get the number of intervals.Write final function: Write the final function. Using the values from the previous steps, the function that models the number of remaining bacteria t seconds since the medicine was introduced is: N(t) = 11,880 * (3/4)^(t/44)

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