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

From the equation obtained using the transformed variables:

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

We can exponentiate to find:

$y = 10^{-1.82} imes x^{0.89}$

Calculating the constant:

$10^{-1.82} \approx 0.015$

Therefore, we can express the relationship as:

$y = 0.015x^{0.89}$

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