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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.

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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

$$f(n+1)-f(n)=\big(a+b(n+1)\big)-(a+bn)=\dots ?$$

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 $a=\dots$?

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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.

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okay thanks man i have another question i dont get – james Apr 6 '13 at 20:28
If a person puts 1 cent in a piggy bank on the first day, 2 cents on the second day, 3 cents on the third day, and so forth, how much money will be in the bank after 40 days? – james Apr 6 '13 at 20:29
@james: For the cents problem, use the formula $\sum_{k=1}^{n}k=\frac{n(n+1)}{2}$. – Mhenni Benghorbal Apr 6 '13 at 20:35

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