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# A Total Emissions Goal

The warming caused by carbon dioxide (CO₂) emissions over any given period is proportional to the total amount of CO₂ emitted over that period. Recognising this, a country decides to limit its carbon dioxide emissions to less than 12×10¹²kg in total emitted across 20 years.

For the first 4 years, the countries emissions are stable at 800×10⁹kg year⁻¹

The country decides that they will be able to reduce their emissions so that each subsequent year produces 5% less emissions than the previous year.

Using the model,

a) Show that the country’s total CO₂ emissions from the
first 6 years are estimated to be 4682×10⁹kg CO₂

[2 marks]

Show that the estimated total emissions per year in the rᵗʰ year, with units
x10⁹kg year⁻¹, for 5 ≤ r ≤ 20, is

800 x 0.95ʳ⁻⁴

[1 mark]

Determine whether the country will meet their 20 year emissions goal.

[4 marks]

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