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3.07 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

ACMGM070

use arithmetic sequences to model and analyse practical situations involving linear growth or decay; for example, 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

ACMGM074

use geometric sequences to model and analyse (numerically, or graphically only) practical problems involving geometric growth and decay; for example, analysing a compound interest loan or investment, the growth of a bacterial population that doubles in size each hour, 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

ACMGM077

use first-order linear recurrence relations to model and analyse (numerically or graphically only) practical problems; for example, investigating the growth of a trout population in a lake recorded at the end of each year and where limited recreational fishing is permitted, or the amount owing on a reducing balance loan after each payment is made

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