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Infer and compare growth or decay rules using exact common-base values.
Free examples and worked answers. No account needed.
Practise the method.
Infer and compare growth or decay rules using exact common-base values.
Infer and compare growth or decay rules using exact common-base values.
Example 1
A culture grows by the same factor each hour. It has 12 cells at hour 1 and 108 at hour 3. At which hour does it first have 324 cells?
Show worked answer
Answer: 4
- Two hours multiply the population by 9
- each hour multiplies by 3.
- At hour 0 there are 4 cells.
- Solve 4×3t=324:t=4.
Example 2
A sample loses the same fraction each hour. It contains 13122 mg at hour 0 and 1458 mg at hour 2. After how many hours does it contain 6 mg?
Show worked answer
Answer: 7
- Over two hours it retains 91
- it retains 31 each hour.
- Solve 3t13122=6;
- since 2187=37,t=7.
Example 3
A culture grows by the same factor each hour. It has 9 cells at hour 1 and 81 at hour 3. At which hour does it first have 243 cells?
Show worked answer
Answer: 4
- Two hours multiply the population by 9
- each hour multiplies by 3.
- At hour 0 there are 3 cells.
- Solve 3×3t=243:t=4.
Put it into practice.
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