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The table lists the number of species of birds on islands of various sizes. Find values for a and b so that y = a + blog x models these data. Estimate the size of an island that might have 14 species of birds. a) b) a) a = ,b= (Type integers or decimals.)

The table lists the number of species of birds on islands of various sizes. Find values for a and b so that y = a + blog x models these data. Estimate the size of an island that might have 14 species of birds. a) b) a) a = ,b= (Type integers or decimals.)

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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The image presents a mathematical problem related to the number of bird species on islands of different sizes. ### Problem Statement The table provides the number of bird species on islands with various areas. Your tasks are: #### (a) To find values for `a` and `b` so that the equation \( y = a + b \log x \) fits the given data. #### (b) Estimate the area of an island that might have 14 species of birds. ### Data Table - **Area (\( \text{km}^2 \))**: \(0.1, 1, 10, 100\) - **Species of birds**: \(7, 9, 11, 13\) ### Instructions for Part (a): You are required to enter the calculated values of `a` and `b` where prompted. Make sure to type them as either integers or decimals. ### Educational Approach This problem is an application of logarithmic regression, where you will apply your knowledge of logarithms to model ecological data. You are expected to use the given data points to find the values of `a` and `b`, giving insight into how bird species diversity correlates with island size. In part (b), you will apply this model to predict conditions not explicitly provided in the data, using the equation derived in part (a).
Transcribed Image Text:The image presents a mathematical problem related to the number of bird species on islands of different sizes. ### Problem Statement The table provides the number of bird species on islands with various areas. Your tasks are: #### (a) To find values for `a` and `b` so that the equation \( y = a + b \log x \) fits the given data. #### (b) Estimate the area of an island that might have 14 species of birds. ### Data Table - **Area (\( \text{km}^2 \))**: \(0.1, 1, 10, 100\) - **Species of birds**: \(7, 9, 11, 13\) ### Instructions for Part (a): You are required to enter the calculated values of `a` and `b` where prompted. Make sure to type them as either integers or decimals. ### Educational Approach This problem is an application of logarithmic regression, where you will apply your knowledge of logarithms to model ecological data. You are expected to use the given data points to find the values of `a` and `b`, giving insight into how bird species diversity correlates with island size. In part (b), you will apply this model to predict conditions not explicitly provided in the data, using the equation derived in part (a).
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