Question

Using the figure, determine the percentage of bird species that will be lost if the island's inhabitable land area is reduced from $100,000{\text{km}}^2$ to $1{\text{km}}^2$. Take slope = 0.15.

• A. 17 percent of the bird species will be lost
• B. 20 percent of the bird species will be lost
• C. All of the bird species will be lost
• D. 93 percent of the bird species will be lost

Answer 1

The correct option is A 17 percent of the bird species will be lost

$\log S=\log C+Z\log Ai.e.,S=C{A}^Z$
where $S=$ Number of bird species
$A=$ Area
$Z=$ Slope of the line (reqression coefficient)$=0.15$
$C=$ y intercept
Area changes from = $100,000{\text{km}}^2$ to $1{\text{m}}^2$
$\frac{S_1=C{A}_1^z}{S_2=C{A}_2^z}$ or ${\left(\frac{C{A}_1}{C{A}_2}\right)}^z$
$\frac{S_2}{S_1}={\left(\frac{A_2}{A_1}\right)}^z$
$\frac{S_2}{S_1}={\left(\frac{1}{100,000}\right)}^{0.15}$
$\frac{S_2}{S_1}=({10}^{-5}{)}^{0.15}$
$\frac{S_2}{S_1}={10}^{-0.75}$
$\frac{S_2}{S_1}=0.17$

Hence, the required precentage = $\frac{S_2}{S_1}=0.17$ X 100% = 17%.