Please help! This one's a thumper and everyone (all my excel 'genius' friends) are stumped. And we may be doing this wrong but if anyone can shed light, would be extremely grateful.
We are given a few numbers to start with:
100,000 This is our "overall" goal (number of calls to be made).
20 This is the number of "week" we have to reach our overall goal.
500 This is the goal for Week 1
With those numbers, we need to come up with weekly goals for 20 weeks that total 100,000 (for example):
Week, Goal
1, 500
2, 603
3, 727 ... and so forth
The trick is that these goals "cannot" be created on a linear path but rather need to be created on a exponential curving growth path. In other words, the goals will start low and over time create a curving increase.
Step I would assume is figuring out the goals with only 100,000 total, 500 start, and 20 weeks. This is where we got lost. So I worked backward to try and see how is "should" look.
So I hard coded a percentage of 20.5682366195176% for each week and this number works perfect when applied to the next weeks goal. I.E. It is this 20.5682366195176% that we're trying to find a formula for given ONLY the numbers we have from the beginning.
For example, see list below:
500 x 20.5682366195176% = 603
603 minus 500 = 103
103 divided by 500 = 20.5682366195176%
If you plot the "goal" numbers on a graph, you get a nice exponential growth curve. As well as, if you add ALL the goals up, you get 100,000. So finding the 20.5682366195176% is the key. But is it possible???
Week, Goal, Growth, %
1, 500,
2, 603, 103, 20.5682366195176%
3, 727, 124, 20.5682366195176%
4, 876, 149, 20.5682366195176%
5, 1,057, 180, 20.5682366195176%
6, 1,274, 217, 20.5682366195176%
7, 1,536, 262, 20.5682366195176%
8, 1,852, 316, 20.5682366195176%
9, 2,233, 381, 20.5682366195176%
10, 2,692, 459, 20.5682366195176%
11, 3,246, 554, 20.5682366195176%
12, 3,913, 668, 20.5682366195176%
13, 4,718, 805, 20.5682366195176%
14, 5,689, 970, 20.5682366195176%
15, 6,859, 1,170, 20.5682366195176%
16, 8,269, 1,411, 20.5682366195176%
17, 9,970, 1,701, 20.5682366195176%
18, 12,021, 2,051, 20.5682366195176%
19, 14,493, 2,472, 20.5682366195176%
20, 17,474, 2,981, 20.5682366195176%
So if we can figure out the formula to get 20.5682366195176%, we can then apply that to create the weekly goals and thus also have our curving growth all in one.
Thanks for any help out there..
We are given a few numbers to start with:
100,000 This is our "overall" goal (number of calls to be made).
20 This is the number of "week" we have to reach our overall goal.
500 This is the goal for Week 1
With those numbers, we need to come up with weekly goals for 20 weeks that total 100,000 (for example):
Week, Goal
1, 500
2, 603
3, 727 ... and so forth
The trick is that these goals "cannot" be created on a linear path but rather need to be created on a exponential curving growth path. In other words, the goals will start low and over time create a curving increase.
Step I would assume is figuring out the goals with only 100,000 total, 500 start, and 20 weeks. This is where we got lost. So I worked backward to try and see how is "should" look.
So I hard coded a percentage of 20.5682366195176% for each week and this number works perfect when applied to the next weeks goal. I.E. It is this 20.5682366195176% that we're trying to find a formula for given ONLY the numbers we have from the beginning.
For example, see list below:
500 x 20.5682366195176% = 603
603 minus 500 = 103
103 divided by 500 = 20.5682366195176%
If you plot the "goal" numbers on a graph, you get a nice exponential growth curve. As well as, if you add ALL the goals up, you get 100,000. So finding the 20.5682366195176% is the key. But is it possible???
Week, Goal, Growth, %
1, 500,
2, 603, 103, 20.5682366195176%
3, 727, 124, 20.5682366195176%
4, 876, 149, 20.5682366195176%
5, 1,057, 180, 20.5682366195176%
6, 1,274, 217, 20.5682366195176%
7, 1,536, 262, 20.5682366195176%
8, 1,852, 316, 20.5682366195176%
9, 2,233, 381, 20.5682366195176%
10, 2,692, 459, 20.5682366195176%
11, 3,246, 554, 20.5682366195176%
12, 3,913, 668, 20.5682366195176%
13, 4,718, 805, 20.5682366195176%
14, 5,689, 970, 20.5682366195176%
15, 6,859, 1,170, 20.5682366195176%
16, 8,269, 1,411, 20.5682366195176%
17, 9,970, 1,701, 20.5682366195176%
18, 12,021, 2,051, 20.5682366195176%
19, 14,493, 2,472, 20.5682366195176%
20, 17,474, 2,981, 20.5682366195176%
So if we can figure out the formula to get 20.5682366195176%, we can then apply that to create the weekly goals and thus also have our curving growth all in one.
Thanks for any help out there..
