Answer:
The number of bacteria [tex]B[/tex] after [tex]d[/tex] days is given by
[tex]B = B_0 (3)^{\frac{1}{10} d}[/tex]
where [tex]B_0[/tex] is the initial number of bacteria.
Step-by-step explanation:
The number of bacteria [tex]B[/tex] in the sample triples every 10 days, this means after the first 10th day, the number of bacteria is
[tex]B = B_0 *3,[/tex]
where [tex]B_0[/tex] is the initial number of bacteria in the sample.
After the 2nd 10th days, the number of bacteria is
[tex]B = (B_0 *3)*3[/tex]
after the 3rd day,
[tex]B =( B_0 *3*3)*3[/tex]
and so on.
Thus, the formula we get for the number of bacteria after the nth 10-days is
[tex]B = B_0 (3)^n[/tex]
where [tex]n[/tex] is is the nth 10-days.
Since, [tex]n[/tex] is 10 days, we have
[tex]d =10n[/tex]
or
[tex]n =\dfrac{1}{10}[/tex]
Substituting that into [tex]B = B_0 (3)^n[/tex], we get:
[tex]\boxed{ B = B_0 (3)^{\frac{1}{10} d}}[/tex]
The daily rate of the bacteria growth is [tex]3^\frac{x}{10}[/tex]
An exponential growth is in the form:
y = abˣ;
where y, x are variables, a is the initial value of y and b > 1
Let y represent the number of bacteria after x days.
The sample triples in 10 days. hence:
b = 3
The equation becomes:
[tex]y=a3^{\frac{1}{10} x}=a.3^{\frac{x}{10} }[/tex]
Therefore the daily rate is [tex]3^\frac{x}{10}[/tex]
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