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Barbara is investigating the relationship between average income (GDP per capita), x US dollars, and average annual carbon dioxide (CO₂) emissions, y tonnes, for different countries - Edexcel - A-Level Maths Statistics - Question 3 - 2019 - Paper 1

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Barbara is investigating the relationship between average income (GDP per capita), x US dollars, and average annual carbon dioxide (CO₂) emissions, y tonnes, for dif... show full transcript

Worked Solution & Example Answer:Barbara is investigating the relationship between average income (GDP per capita), x US dollars, and average annual carbon dioxide (CO₂) emissions, y tonnes, for different countries - Edexcel - A-Level Maths Statistics - Question 3 - 2019 - Paper 1

Step 1

Show that the relationship between y and x can be written in the form y = ax^b where a and b are constants to be found.

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Answer

From the equation obtained using the transformed variables:

log10y=1.82+0.89log10x\log_{10}y = -1.82 + 0.89 \log_{10}x

We can exponentiate to find:

y=101.82imesx0.89y = 10^{-1.82} imes x^{0.89}

Calculating the constant:

101.820.01510^{-1.82} \approx 0.015

Therefore, we can express the relationship as:

y=0.015x0.89y = 0.015x^{0.89}

This shows that y can be modeled as a function of x in the form required.

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