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lyzab19
21.04.2021 •
Mathematics
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Ответ:
a).![P_{t}=\frac{5}{3}P_{t-1}](/tpl/images/0075/6986/091d3.png)
b).![A_{t}=300e^{0.1277\times t}](/tpl/images/0075/6986/7c377.png)
c). 6429 bacteria
Step-by-step explanation:
Population of the bacteria grows exponentially.
Therefore, growth of the bacteria will be represented by the formula
Where
= Population of the bacteria after time t
k = growth constant
t = time taken for growth
Now we plug in the values in the formula
Time t = 4 hours
Now we take the natural log (ln) on both the sides
4k(lne) = ln(500) - ln(300)
4k = 6.2146 - 5.7038
4k = 0.5108
k =![k=\frac{0.5108}{4}=0.1277](/tpl/images/0075/6986/74acd.png)
a). Recursive formula for the sequence formed by the bacterial growth
Since![P_{t}=(1+r)P_{t-1}](/tpl/images/0075/6986/1a49a.png)
500 = (1 + r)300
r =![\frac{5}{3}-1=\frac{2}{3}](/tpl/images/0075/6986/578c4.png)
Therefore, the recursive formula will be
b). Explicit formula for the number of the bacteria will be
c). We have to calculate the number of bacteria after 24 hours