Question

To predict the number of species (n) that live in a region of some area (A), biologists use the logarithmic model n = k log A, where k is some constant. If 5,800 species live in a rain forest that has an area of 750 square kilometers (km2), approximately how many species will be left after half of the rain forest is destroyed due to an amusement park being built there? Hint: First you need to solve for the constant k.

Answer 1

n = 5192 species remain

Explanation:

Solving for k

5800 = k log 750

5800 = k(2.875)

k = 5800 / 2.87506

k = 2017.35

Substituting the value of k we get

n= k log A / 2

n = 2017.35 log (750/2)

n = 2017.35 (2.574)

n = 5192 species remain

Answer 2

There are 5193 species will be left

Explanation:

* Lets explain how to solve the problem

- The number of species (n) that live in a region of some area (A), can

be found by using the logarithmic model n = k log A where k is

a constant

- If 5,800 species live in a rain forest that has an area of 750 square

kilometers

∴ n = 5800 species

∴ A = 750 km²

- Substitute the value of A and n in the equation to fined k

∵ A = 750 , n = 5800

∵ n = k log A

∴ 5800 = k log (750)

- Divide both sides by log (750)

∴ k = 5800 ÷ log (750)

∴ k = 2017.34

- Lets substitute the value of k in the equation

∴ n = 2017.34 log A

- The half of the rain forest is destroyed due to an amusement park

being built there

∴ The new area is 1/2 the old area

∵ The old area is 750

∴ The new area = 1/2 × 750 = 375 km²

- Lets substitute this value in the equation to find the number of

species will be left in the new area

∵ A = 375

∴ n = 2017.34 log (375) = 5192.696 ≅ 5193

∴ There are 5193 species will be left