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Maru [420]
2 years ago
12

80 POINTSSSSS

Mathematics
1 answer:
Semenov [28]2 years ago
7 0

Answer:

Tawny Eagle

Step-by-step explanation:

<u>Percent Change Formula</u>

\sf percent\:change=\dfrac{final\:value-initial\:value}{initial\:value} \times 100

<u>African Fish Eagle</u>

Given:

  • Initial population = 32,800
  • Final population = 43,952

\implies \sf percent\:change=\dfrac{43952-32800}{32800} \times 100=34 \%

<u>Tawny Eagle</u>

Given:

  • Initial population = 7,900
  • Final population = 10,981

\implies \sf percent\:change=\dfrac{10981-7900}{7900} \times 100=39 \%

<u>Solution</u>

Therefore, the Tawny Eagle species saw a larger percent increase to their population over the last 8 years.

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xyz = \left(1 + \dfrac{\ln(c)}{\ln(b)}\right) \left(1 + \dfrac{\ln(a)}{\ln(c)}\right) \left(1 + \dfrac{\ln(b)}{\ln(a)}\right)

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xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} \\\\ ~~~~~~~~~~~~+ \dfrac{\ln(c)\ln(a)}{\ln(b)\ln(c)} + \dfrac{\ln(c)\ln(b)}{\ln(b)\ln(a)} + \dfrac{\ln(a)\ln(b)}{\ln(c)\ln(a)} \\\\ ~~~~~~~~~~~~ + \dfrac{\ln(c)\ln(a)\ln(b)}{\ln(b)\ln(c)\ln(a)}

Simplify and rewrite using the logarithm properties mentioned earlier.

xyz = 1 + \dfrac{\ln(c)}{\ln(b)} + \dfrac{\ln(a)}{\ln(c)} + \dfrac{\ln(b)}{\ln(a)} + \dfrac{\ln(a)}{\ln(b)} + \dfrac{\ln(c)}{\ln(a)} + \dfrac{\ln(b)}{\ln(c)} + 1

xyz = 2 + \dfrac{\ln(c)+\ln(a)}{\ln(b)} + \dfrac{\ln(a)+\ln(b)}{\ln(c)} + \dfrac{\ln(b)+\ln(c)}{\ln(a)}

xyz = 2 + \dfrac{\ln(ac)}{\ln(b)} + \dfrac{\ln(ab)}{\ln(c)} + \dfrac{\ln(bc)}{\ln(a)}

xyz = 2 + \log_b(ac) + \log_c(ab) + \log_a(bc)

\implies \boxed{xyz = x + y + z + 2}

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