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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.

Respuesta :

calculista

Answer:

[tex]N(t)=11,880(\frac{3}{4} )^{\frac{t}{44}}[/tex]

Step-by-step explanation:

we know that

The equation of a exponential decay function is given by

[tex]N(t)=a(1-r)^t[/tex]

where

N(t) is the number of remaining bacteria

t is the time in seconds every 44 seconds

a is the initial value

r is the rate of change

we have

[tex]a=11,880\ bacteria\\r=1/4[/tex]

substitute

[tex]N(t)=11,880(1-\frac{1}{4} )^{\frac{t}{44}}[/tex]

[tex]N(t)=11,880(\frac{3}{4} )^{\frac{t}{44}}[/tex]