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Without the addition of fertiliser, the annual crop from a potato farm would only be80% of the previous year’s crop. A farm produced 15 tonnes of potatoes in its first yearof production. Assume that no fertiliser is used. Give answers correct to two decimalplaces where necessary.a List the size of the potato crop for each of the first 4 years.b What will be the total potato production for the first 4 years?c In which year would the annual potato crop be less than a third of the cropproduced in the first year?

Question

Without the addition of fertiliser, the annual crop from a potato farm would only be80% of the previous year’s crop. A farm produced 15 tonnes of potatoes in its first yearof production. Assume that no fertiliser is used. Give answers correct to two decimalplaces where necessary.a List the size of the potato crop for each of the first 4 years.b What will be the total potato production for the first 4 years?c In which year would the annual potato crop be less than a third of the cropproduced in the first year?

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Solution

a. The size of the potato crop for each of the first 4 years would be as follows:

  • Year 1: 15 tonnes
  • Year 2: 80% of 15 tonnes = 12 tonnes
  • Year 3: 80% of 12 tonnes = 9.6 tonnes
  • Year 4: 80% of 9.6 tonnes = 7.68 tonnes

b. The total potato production for the first 4 years would be the sum of the annual crops from each year. So, 15 tonnes (Year 1) + 12 tonnes (Year 2) + 9.6 tonnes (Year 3) + 7.68 tonnes (Year 4) = 44.28 tonnes.

c. The annual potato crop would be less than a third of the crop produced in the first year when it falls below 15 tonnes / 3 = 5 tonnes. Looking at the annual crops calculated in part a, this would occur in the 5th year.

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