A seedling is measured every week. Its height in cm, from week 0 to week 10, is 2, 2.2, 2.6, 4, 8…
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A seedling is measured every week. Its height in cm, from week to week , is 2, 2.2, 2.6, 4, 8, 15, 25, 32, 35, 36 and 36.
- What is the largest gain made in one week?
- What is the total growth over the weeks?
- Which phase of the sigmoid curve is weeks to , and which is weeks and ?
- Why does the growth stop rising near the end?
Need a reminder? The key ideaShow
Arithmetic growth: , a straight line. Geometric growth: , a sigmoid curve with a lag, a log and a stationary phase. Absolute growth rate is the total gain in a unit of time. Relative growth rate is the gain per unit of the starting size. A part that doubles in a time has . Growth needs water, oxygen, nutrients and a suitable temperature.
The worked solution
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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The gains. Week by week, in cm: 0.2, 0.4, 1.4, 4, 7, 10, 7, 3, 1 and 0. The largest is , from week to week .
Step 2. The total. .
Step 3. The phases. Weeks to give gains of only and : the lag phase. The middle weeks, with big gains, are the log phase. Weeks and give almost no gain: the stationary phase.
Step 4. Why growth stops rising. In the stationary phase the nutrients or the space run short, so growth slows and stops.
Answer: ; ; lag phase and stationary phase; nutrients or space run short.
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