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Arithmetic Afforestation

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A country decides to begin a reforestation program, starting in 2020, gradually increasing the number of trees planted per year by the same amount each year.

The timetable for the first four years is shown below:

Year: 2020 2021 2022 2023
Trees planted: 6.0×10 1.4×10 2.2×10 3.0×10

a) Find an expression, in terms of n for the number of trees planted in year n.

[2 marks]

b) Calculate how many trees in total will be planted if this program is followed for 10 years.

[2 mark] 

The government will declare the program a success once 2.45×10 trees have been planted in total

c) Given that the country plants all of the trees that the model would predict in year k, but reaches the target part way through year (k + 1), show that k satisfies 

(2k – 49)(k + 25) < 0.

[5 marks]

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