QuestionHenrietta managed a plantation of pine trees which were grown and sold for their timber. The plantation was developed from an initial planting of 45000 trees, with a net increase, after sales and plantings, of 2500 trees each year over a period of 15 years.
At the beginning of the 16 th year of the plantation, it was decided to sell-off of the trees remaining on the plantation each year for timber, without any further plantings, so that the land could ultimately be used for another purpose.
Questions:
1. How many trees were on the plantation at the beginning of the 5 th year of the plantation?
2. At the beginning of which year of the plantation there were 65000 trees on the plantation?
Studdy Solution
STEP 1
1. The initial number of trees is 45,000.
2. The net increase in the number of trees each year is 2,500.
3. The period of net increase is 15 years.
4. From the 16th year onwards, 40% of the trees are sold off each year without any further plantings.
5. We need to find the number of trees at the beginning of the 5th year.
6. We need to determine the year when the number of trees reaches 65,000.
STEP 2
1. Calculate the number of trees at the beginning of each year up to the 5th year.
2. Determine the year when the number of trees reaches 65,000.
STEP 3
Calculate the number of trees at the beginning of the 1st year.
STEP 4
Calculate the number of trees at the beginning of the 2nd year.
STEP 5
Calculate the number of trees at the beginning of the 3rd year.
STEP 6
Calculate the number of trees at the beginning of the 4th year.
STEP 7
Calculate the number of trees at the beginning of the 5th year.
STEP 8
Set up the equation for the year when the number of trees reaches 65,000.
STEP 9
Solve for when .
STEP 10
Simplify the equation to solve for .
The number of trees at the beginning of the 5th year is 55,000.
The number of trees reaches 65,000 at the beginning of the 9th year.
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