Which Numbers Are Solutions Of H2 + 4 = 8h – 3? - Gauthmath

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Question

There were 500 lions in an African nature reserve. 3 years later there were 864 lions in the same nature reserve. a) Work out the percentage increase per year, assuming that the number of lions increased by the same percentage each year. b) Use your answer to part a) to predict the number of lions in the nature reserve after another year. Round your answer to the nearest integer.SHOW LESS0

Solution

user avatar imageAnswera) 20% b) 1037ExplanationStep 1: Let the percentage increase per year be \( r \). The initial number of lions is 500, and after 3 years, there are 864 lions. Step 2: Set up the equation for the number of lions after 3 years: \( 500(1+r)^3 = 864 \). Step 3: Solve for \( r \) by dividing both sides of the equation by 500 to get \( (1+r)^3 = \frac{864}{500} \). Step 4: Calculate the cube root of \( \frac{864}{500} \) to find \( r \): \( r = \sqrt[3]{\frac{864}{500}} - 1 \). Step 5: Simplify the expression to find \( r \): \( r = 0.2 = 20\% \). Step 6: To predict the number of lions after another year, use the percentage increase from part a) and the number of lions after 3 years: \( 864(1+r) \). Step 7: Calculate the number of lions after another year: \( 864(1+20\%) = 864(1.2) = 1037 \). So, the percentage increase per year is 20%, and after another year, there will be approximately 1037 lions in the nature reserve.Click to rate:39.3(61 votes)Search questionBy textBy image/screenshotDrop your file here orClick Hereto upload

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