A certain species of tree grows an average of 4.2 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 300 centimeters tall.
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
HINT: On average the tree is adding a constant amount, $4.2$ cm, per week; that’s an example of linear growth. Linear growth is described by a function of the form $f(n)=a+bn$, where $n$ is the number of the week. The amount of growth from week $n$ to week $n+1$ is therefore
If you answer that question correctly, you should be able to figure out what $b$ should be for your tree’s growth. And the height at the beginning is the height at week $0$, so $a=\dots$?
Try this. Since the tree starts out a 300 cm and grows 4.2 cm a week, $$h(w) = 300 + 4.2 w,$$ where $w$ is time in weeks.