How many QCAA General Mathematics questions cover Growth and decay in sequences?

AusGrader has 93 QCAA General Mathematics questions on Growth and decay in sequences, all with instant AI grading and detailed marking feedback.

QCAA (QCE) General Mathematics — Growth and decay in sequences Questions & Answers | AusGrader

Q9

2024

QCAA

Paper 1

1 mark

Q9

1 mark

Determine the 4th term for the geometric sequence that begins 1000, -900, ...

A

729

B

700

C

-700

D

-729

Q9

2023

QCAA

Paper 1

1 mark

Q9

1 mark

Determine the 6th term of the arithmetic sequence that begins 3, 9, …

A

21

B

33

C

45

D

729

Q6

2024

QCAA

Paper 2

6 marks

Q6

6 marks

The daily cost (＄) for a person for meals and accommodation is predicted to change according to the cost models shown.

Category	2021 daily cost (＄)	Cost model, where $n$ = number of years after 2020
Meals	$c$	$m_n = m_1 + 3(n-1)$
Accommodation	$2c$	$a_n = a_1 \times 1.1^{(n-1)}$

In 2021, the daily cost for a person's meals was ＄60.

In 2025, the total cost for a person for seven days for meals and accommodation is estimated to be between ＄1500 and ＄2000. Evaluate the reasonableness of the estimate.

Daily cost for a person in 2021 ( $n=1$ ).
$m_1 = c = ＄60$
$a_1 = 2c = ＄120$

In 2025, $n = 5$

Daily cost for a person in 2025 for meals:
$m_n = m_1 + 3(n-1)$
$m_5 = 60 + 3(5-1)$
$= ＄72$

Daily cost for a person in 2025 for accommodation:
$a_n = a_1 \times 1.1^{(n-1)}$
$a_5 = 120 \times 1.1^{(5-1)}$
$= ＄175.69$

Total cost for a person in 2025 for 7 days
$= 72 \times 7 + 175.69 \times 7$
$= ＄1733.83$

$1500 < 1733.83 < 2000$
$\therefore$ The estimate is reasonable as $＄1733.83$ is between $＄1500$ and $＄2000$ .

Marking Criteria

Descriptor	Marks
correctly determines values for $m_1$ and $a_1$	1
correctly determines $n = 5$	1
uses arithmetic model to determine daily cost for a person in 2025 for meals ( $m_5$ )	1
uses geometric model to determine daily cost for a person in 2025 for accommodation ( $a_5$ )	1
calculates total cost for a person in 2025 for 7 days	1
provides appropriate statement of reasonableness linked to prior working	1

Q26

2020

QCAA

Paper 1

5 marks

Q26

A scientist observed that the population of a specific bird species is decreasing by 17% each year and that at the beginning of 2016, there were 483 birds.

Q26a

2 marks

Use a geometric sequence to model the bird population.

Determine the common ratio
$r = 1 - 0.17$
$= 0.83$

Determine the model
let $n =$ the number of years since 2015
and $t_n =$ the number of birds

$t_n = t_1 r^{(n-1)}$
$= 483 \times 0.83^{n-1}$

Marking Criteria

Descriptor	Marks
Correctly determines the common ratio	1
Determines geometric model	1

Q26b

3 marks

Using the model from 26a), predict the number of birds remaining at the beginning of 2021.

$n = 6$
$t_6 = 483 \times 0.83^5$
$= 190.255 ...$

Expect 190 birds remaining.

Marking Criteria

Descriptor	Marks
Correctly determines the $n$ value	1
Determines $t_6$	1
States a reasonable answer	1

Q18

2020

QCAA

Paper 1

4 marks

Q18

Exhibition organisers believe that the number of attendees increases each day as an arithmetic sequence. The organisers know that 353 people attended the first day and 439 people attended the third day.

Q18a

2 marks

Determine the common difference.

Descriptor	Marks
Correctly provides mathematical reasoning to support the answer	1
Correctly determines the common difference	1

Q18b

2 marks

Use the result from 18a) to predict the number of people who will attend the sixth day.

Find $t_6$
$t_6 = t_1 + 5d$
$= 353 + 5 \times 43$
$= 568$

They would expect 568 people to attend the sixth day.

Marking Criteria

Descriptor	Marks
Substitutes into an appropriate rule	1
Determines value	1

QCAA General Mathematics Growth and decay in sequences

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