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sofia5044
02.04.2020 •
Mathematics
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 \dfrac 14 4 1 start fraction, 1, divided by, 4, end fraction of its size every 444444 seconds. The number of remaining bacteria can be modeled by a function, NNN, which depends on the amount of time, ttt (in seconds). Before the medicine was introduced, there were 11{,}88011,88011, comma, 880 bacteria in the Petri dish. Write a function that models the number of remaining bacteria ttt seconds since the medicine was introduced.
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Ответ:
Function:![N(t)=11,800*0.75^{\frac{t}{4}}](/tpl/images/0577/3307/876a7.png)
Step-by-step explanation:
The population loses 1/4th every 4 seconds, amount of original.
Initial amount of bacteria was 11,880
1/4 = 0.25
Looses 0.25 so that means 1 - 0.25 = 0.75 remaining of total every 4 seconds
We can model using exponential equation of the form:
Where
C is the initial amount (given as 11,880)
I is the remaining factor, we found to be 0.75
n is the seconds it takes to go to 0.75 of its original, n = 4 because it is given in 4 seconds
Now, substituting, we find the equation:
Ответ:
thansk