A town council compares two growth rates for the next few decades: 1.5% a year and 2.5% a year…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A town council compares two growth rates for the next few decades: a year and a year.
- What is the doubling time at a year?
- What is the doubling time at a year?
- How many times longer is the first time than the second?
- The council uses the rule of 70 for a quick check. What does it give for each rate?
Need a reminder? The key ideaShow
A population that grows by per cent a year is multiplied by every year. After years: . The doubling time is , close to years. The growth in a year, per people, is the birth rate minus the death rate.
The worked solution
Have you tried it?
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.
Given. Rates and a year.
Plan. Use the exact formula, then the rule of 70 as a check.
Step 1. The first rate. years.
Step 2. The second rate. years.
Step 3. The ratio. .
Step 4. The rule of 70. years and years.
Answer: years; years; times; years and years.
Check. The rule is close for both rates. It is a little less exact when the rate is larger.
What if? At a year the doubling time is years.
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