Practice: growth and decay
Practice: growth and decay
A culture in a laboratory has 2,500 bacteria.
The number of bacteria grows by 40% every hour.
What is the growth factor?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
How many bacteria will the culture have after 3 hours?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A patient’s blood holds 600 mg of a medicine.
Every hour the amount in the blood shrinks by 25%.
How many mg will be in the blood after two hours?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
How many mg will be in the blood after 6 hours? Round to a whole number.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Another patient was given the same medicine. An hour later 450 mg were left in his blood.
Write an equation and solve it: how many mg was he given?
Medical scans use a radioactive substance, technetium-99m.
Its half-life is 6 hours.
A patient was given 40 micrograms.
How many micrograms will be left after 24 hours?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
How many micrograms will be left after 9 hours? Round to one decimal place.
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/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
The number of users of hired electric scooters in a city, each year:
| Year | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Users | 1,500 | 1,800 | 2,160 | 2,592 |
What is the growth factor?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
By what percentage does the number of users grow every year?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
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If the growth goes on like this, how many users will there be in year 6? Round to a whole number.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
The graph: the amount of a radioactive substance, in grams, each week – .
Mark the amount at the start, and the point where 100 grams are left.
Algae are spreading in two ponds.
In pond A the algae cover 10 m², and 6 m² are added every week.
In pond B the algae cover 10 m², and their area grows by 30% every week.
How many m² will the algae in pond A cover after 8 weeks?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
How many m² will the algae in pond B cover after 8 weeks? Round to one decimal place.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
In which pond will the algae spread faster from then on? Explain.
Coffee is poured at 85 degrees, in a room at 25 degrees.
Every minute the difference between the coffee and the room shrinks by 8%.
What is the temperature of the coffee after 10 minutes? Round to one decimal place.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power