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Chapter 6: Problem 8

The World Wildlife Fund (WWF) estimated that in 2001 the world tiger population was between 5000 and \(7000 .\) Accurate data is difficult to obtain but one estimate is that this is a \(95 \%\) reduction from the tiger population in 1900 . a. What is a lower-range estimate for the tiger population in \(1900 ?\) b. What is an upper-range estimate for the tiger population in \(1900 ?\)

Short Answer

Expert verified
The lower-range estimate for the tiger population in 1900 is 100,000, and the upper-range estimate for the tiger population in 1900 is 140,000.

Step by step solution

01

Find the original population based on the percentage reduction

Since the population in 2001 represents a 95% reduction from the population in 1900, we know that only 5% of the 1900 tiger population survive in 2001. To find the 1900 population, we need to calculate what the 2001 estimates represent as 5%. We will do this for the lower-range (5,000) and the upper-range (7,000) estimates.
02

Calculate the lower-range estimate for the 1900 tiger population

To find the lower-range estimate of the 1900 population, we will first calculate the value that represents 5% of the population for the lower estimate of 5,000. Let the lower-range tiger population in 1900 be \(x\). We can express the given information as: 5% of \(x\) = 5,000 We can write this equation as: \(\frac{5}{100}x = 5000\) Now, to solve for \(x\), we can multiply both sides of the equation by \(\frac{100}{5}\): \(x = 5000 \times \frac{100}{5}\) Calculating the value: \(x = 5000 \times 20\) \(x = 100,000\) The lower-range estimate for the tiger population in 1900 is 100,000.
03

Calculate the upper-range estimate for the 1900 tiger population

Next, we will do the same calculation for the upper-range estimate, which is 7,000. Let the upper-range tiger population in 1900 be \(y\). We can express the given information as: 5% of \(y\) = 7,000 We can write this equation as: \(\frac{5}{100}y = 7000\) Now, to solve for \(y\), we can multiply both sides of the equation by \(\frac{100}{5}\): \(y = 7000 \times \frac{100}{5}\) Calculating the value: \(y = 7000 \times 20\) \(y = 140,000\) The upper-range estimate for the tiger population in 1900 is 140,000.
04

Results

In conclusion, the lower-range estimate for the tiger population in 1900 is 100,000 and the upper-range estimate for the tiger population in 1900 is 140,000.

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