A. B(x)=2000000(3)^x
B.B(1.4)= 9311073 million per milliliter
Step-by-step explanation:
A.
The exponential formula to apply is;
[tex]y=Ab^t[/tex]
The starting amount =2000000, =A
The concentration triples each week, thus to find b, use x=1 and y=6000000 (concentration triple after each week)
Substitute in the formula as;
6000000=2000000*b¹
6=2*b¹
3=b¹
3=b
The exponential model is:
[tex]y=2000000(3)^t[/tex]
B(x)=2000000(3)^x
B.
The estimate concentration of bacteria after 1.4 weeks will be;
[tex]y=2000000*3^{1.4} \\\\\\y=2000000*4.66\\\\y=9311073[/tex]
B(1.4)= 9311073 million per milliliter
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Keywords : sample, bacteria, river, initial concentration, triples, week, exponential model,estimate
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The estimated concentration of bacteria after 1.4 weeks 5.488 million per milliliter
An exponential growth is given by:
y = abˣ
where y, x are variables, a is the initial value of y and b is the multiplier.
Let B(x) represent the concentration after x weeks.
a)
Since a river has an initial concentration of 2 million bacteria per milliliter and its concentration triples each week. Hence a = 2000000, b = 3, hence:
[tex]B(x)=2000000(3)^x[/tex]
b) the estimated concentration of bacteria after 1.4 weeks :
[tex]B(1.4)=2000000(1.4)^3=5488000[/tex]
The estimated concentration of bacteria after 1.4 weeks 5.488 million per milliliter
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