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High and low frequency a porpoise can hear are 1.5 x10^5 and 7.5 x 10^1. Which is a reasonable estimate of the quotient of the highest and lowest audible for the porpoise?
A. 10,000,000 and 100,000,000
B. 1000 and 10,000
C. 100,000 and 1,000,000
D. 10,000 and 100,000

Respuesta :

The orders of magnitude of the highest and lowest frequencies are [tex]10^5[/tex] and [tex]10^1[/tex]. This means that their ratio is

[tex]\dfrac{10^5}{10^1}=10^4=10000[/tex]

Since the highest frequency has the lesser coefficient, the ratio will be less than 10.000. So, an estimate can be "between 1.000 and 10.000"

For the record, the answer is

[tex]\dfrac{1.5\cdot 10^5}{7.5\cdot 10^1} = 0.2\cdot 10^4 = 2.000[/tex]

which is indeed between 1.000 and 10.000.

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