Math 1 · Unit 9 · Lesson 5 · part 4 of 5
The orchard: cross out the wrong rules
An orchard starts with 4 trees (year 0).
The orchard: cross out the wrong rules
An orchard starts with 4 trees (year 0). The owner plants the same number of trees every year, and in year 29 there are 178 trees. Which rule gives the number of trees in year n?
You can work it out: 178 − 4 = 174 trees were added in 29 years, and 174 ÷ 29 = 6 trees a year, so t(n) = 6n + 4. On a test you can also cross out the rules that cannot be right, the elimination habit from Unit 3, Lesson 3. Try it: pick any choice to see what rules it out.
Why n and not n − 1 here?The orchard's first input is year 0, so year n is n steps from the start: t(n) = 4 + 6n. If the same orchard were numbered from year 1 (4 trees in year 1), the rule would be 4 + 6(n − 1). The list is the same; only the numbering changes. That is why you always ask where the counting starts.