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3.06 Further applications of growth and decay

Interactive practice questions

A diving vessel descends below the surface of the water at a constant rate so that the depth of the vessel after $1$1 minute, $2$2 minutes and $3$3 minutes is $50$50 metres, $100$100 metres and $150$150 metres respectively.

a

By how much is the depth increasing each minute?

b

What will the depth of the vessel be after $4$4 minutes?

c

Continuing at this rate, what will be the depth of the vessel after $10$10 minutes?

Easy
1min

A paver needs to pave a floor with an area of $800$800 square metres. He can pave $50$50 square metres a day.

Easy
1min

For a fibre-optic cable service, Christa pays a one off amount of $\$200$$200 for installation costs and then a monthly fee of $\$30$$30.

Easy
3min

A diving vessel descends below the surface of the water at a constant rate so that the depth of the vessel after $4$4 minutes, $8$8 minutes and $12$12 minutes is $5$5 metres, $10$10 metres and $15$15 metres respectively.

If $n$n is the number of minutes it takes to reach a depth of $40$40 metres, solve for $n$n.

Easy
3min
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Outcomes

3.3.1.4

use arithmetic sequences to model and analyse practical situations involving linear growth or decay, such as analysing a simple interest loan or investment, calculating a taxi fare based on the flag fall and the charge per kilometre, or calculating the value of an office photocopier at the end of each year using the straight-line method or the unit cost method of depreciation

3.3.2.4

use geometric sequences to model and analyse (numerically or graphically only) practical problems involving geometric growth and decay (logarithmic solutions not required), such as analysing a compound interest loan or investment, the growth of a bacterial population that doubles in size each hour or the decreasing height of the bounce of a ball at each bounce; or calculating the value of office furniture at the end of each year using the declining (reducing) balance method to depreciate

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