Calculating task reduction rate over time, accounting for task growth rate

[elkay_brooklyn]

This seems like it should be easy, but I can't quite figure it out.

Situation: there is a backlog of tasks, and new tasks continue to be added to the list at a steady rate. Assuming I know the starting number of tasks, the growth rate, and the number of hours that can be allocated to the backlog, how do I calculate the amount of time it will take to get the backlog number to 15? or to 0?

Concrete example:
There are 130 tasks to do (backlog list)
Staff can do 40 tasks per week.
Every week 30 new tasks are added to the backlog list.
How many weeks will it take to get the number of tasks on the backlog list down to 15?

 

[DRSteele]

Welcome to the forum.

If I understand correctly, this ought to do it.

	A	B	C
Backlog	tasks
Staff work, per week
New, per week
Net, per week
Floor	tasks
Required	weeks

<colgroup><col style="width: 25pxpx"><col><col><col></colgroup><thead>
</thead><tbody>
[TD="align: center"]2[/TD]

[TD="align: right"]130[/TD]

[TD="align: center"]3[/TD]

[TD="align: right"]-40[/TD]
[TD="align: right"][/TD]

[TD="align: center"]4[/TD]

[TD="align: right"]30[/TD]
[TD="align: right"][/TD]

[TD="align: center"]5[/TD]

[TD="align: right"]-10[/TD]
[TD="align: right"][/TD]

[TD="align: center"]6[/TD]

[TD="align: right"]15[/TD]

[TD="align: center"]7[/TD]

[TD="align: right"]12[/TD]

</tbody>

Sheet31​

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