Geometric series - practical application 2 - Numbas at mathcentre.ac.uk

Error

There was an error loading the page.

Contributors

History

○

Xiaodan Leng 5 years, 9 months ago

Created this as a copy of Geometric series - practical application 2.

Name	Status	Author	Last Modified
Geometric series - practical application	Ready to use	joshua boddy	01/06/2016 09:47
Geometric series - practical application 2	Ready to use	joshua boddy	01/06/2016 09:47
Jinhua's copy of Geometric series - practical application	Ready to use	Jinhua Mathias	28/08/2024 12:15
Jinhua's copy of Geometric series - practical application 2	Ready to use	Jinhua Mathias	28/08/2024 12:15
Geometric series - practical application	draft	Xiaodan Leng	11/07/2019 05:31
Geometric series - practical application	draft	Xiaodan Leng	11/07/2019 06:52
Geometric series - practical application 2	draft	Xiaodan Leng	11/07/2019 06:53

Question statement

A pump is used to extract air from a bottle. The first operation of the pump extracts $\var{n}$ cm $^3$ of air and subsequent extractions follow a geometric series. Extraction number $\var{dayn}$ of the pump extracts $\simplify{{n}*{m}^({dayn}-1)}$ cm $^3$ of air.

Give any introductory information the student needs.

			Name	Type	Generated Value

dur	integer	10
n	integer	40
m1	integer	3
m2	integer	4
m	rational	2/3
dayn	integer	4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(10..50)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

Advice

The $n$ ^th term in a geometric progression is given by $a_1 \times r^{n-1}$ where $a_1$ is the first term and $r$ is the common ratio.

We are given that the first term is $\var{n}$ and the $\var{dayn}$ ^th term is $\simplify{{n}*{m}^({dayn}-1)}$

Hence we know that $r^{\var{dayn}-1} = \frac{\simplify{{n}*{m}^({dayn}-1)}}{\var{n}} = \simplify{{m}^({dayn}-1)}$

So we find that $r=\var{m}$

If the pump were to extract air indefinitely, we look to the formula $S_n = \frac{a_1}{1-r}$ to find $S_n = \frac{\var{n}}{1-\var{m}} = \simplify{{n}/(1-{m})}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Mathematical expression
Mathematical expression		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet

This question is not used in any exams.

Loading...

Error

Geometric series - practical application 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Loading...

Error

Geometric series - practical application 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 9 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Mathematical expression

Advanced settings

Checking accuracy

Variable value generators

Pattern restriction

Variables

String restrictions

Generated value: `integer`