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6.04 Practical applications of arithmetic sequences

Interactive practice questions

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

a

Complete the table showing the area left to pave at the start of each day:

Day Area of floor left to pave ($m^2$m2)
$1$1 $800$800
$2$2 $\editable{}$
$3$3 $\editable{}$
$4$4 $\editable{}$
$5$5 $\editable{}$
b

What type of change is this?

Linear growth

A

Exponential growth

B

Linear decay

C

Exponential decay

D

Linear growth

A

Exponential growth

B

Linear decay

C

Exponential decay

D
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A new lounge suite depreciates by a constant amount each year and its value is modelled by the recurrence relation

$V_{n+1}=V_n-700$Vn+1=Vn700, $V_0=4800$V0=4800

where $V_n$Vn is the value of the lounge suite, in dollars, after $n$n years.

The value of a fridge depreciates by a constant amount each year and is modelled by the recurrence relation

$V_{n+1}=V_n-300$Vn+1=Vn300, $V_0=1600$V0=1600

where $V_n$Vn is the value of the fridge, in dollars, after $n$n years.

The value of an investment that pays simple interest each year is modelled by the recurrence relation

$V_n=V_{n-1}+200$Vn=Vn1+200, $V_0=1000$V0=1000

where $V_n$Vn is the value of the investment after $n$n years.

Outcomes

AoS3.12

Define and explain key concepts in use of a first-order linear recurrence relation to generate the terms of a number sequence, and apply a range of related mathematical routines and procedures

AoS3.15

Define and explain key concepts in use of a recurrence relation to model and analyse practical situations involving discrete linear growth or decay such as a simple interest loan or investment, the depreciating value of an asset using the unit cost method; and the rule for the value of a quantity after n periods of linear growth or decay and its use, and apply a range of related mathematical routines and procedures

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