Blueberry bushes are planted in a field in the year 2009. The blueberry bushes start to grow and cover the field in such a way that the area covered by the bushes doubles every year. If they continue to grow in this way, the field will be entirely covered with blueberry bushes by the year 2016.

When will the field be covered 25% of the way?

The field will be covered 25% of the way in 2015.

The field will be covered 25% of the way in 2013.

The field will be covered 25% of the way in 2014.

The field will be covered 25% of the way in 2012.

Question

Mathematics

Marilyn Weber

3 December, 12:09

Blueberry bushes are planted in a field in the year 2009. The blueberry bushes start to grow and cover the field in such a way that the area covered by the bushes doubles every year. If they continue to grow in this way, the field will be entirely covered with blueberry bushes by the year 2016.

When will the field be covered 25% of the way?

The field will be covered 25% of the way in 2015.

The field will be covered 25% of the way in 2013.

The field will be covered 25% of the way in 2014.

The field will be covered 25% of the way in 2012.

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Answers (1)

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Garrett Holder · Answer 1

We have that 25%=1/4. We have that if in 2016 the full field was covered, in 2015 only half the field was covered. Similarly, in 2014 the ratio of the field that was covered was half that of 2015, so Area of 2014 = 1/2 * (Area of 2015) = 1/2*1/2 * (Area of 2016). Hence, 25% of the field was covered in 2014.