
Exponential Equation
The government of a developing country is implementing a new reading program in which each individual who can read spends one year teaching two others to read. At the end of the year, the original individual can stop, but each of the two people who just learned to read must now spend a year teaching two more people to read. If 1,000 people can read at the start of the program, how can you make a rule or equation to represent this information for year 10?
I am aware of the number of people that can read, however, I am having difficultly representing this as an equation. I am aware of expontial equations, however, I cannot figure this one out.
T= ab^y + b I believe this is the exponential formula.
Year Teachers Learners Total
1 1,000 2,000 3,000
2 2,000 4,000 7,000
3 4,000 8,000 15,000
4 8,000 16,000 31,000
5 16,000 32,000 63,000
6 32,000 64,000 127,000
7 64,000 128,000 255,000
8 128,000 256,000 511,000
9 256,000 512,000 1,023,000
10 512,000 1,024,000 2,047,000
I feel as thought I have the correct information in my formula, and I am sure that I have all of the numbers that need to be used for the exponential formula but just can't seem to get it.
Thanks!
I hope this is in the correct forum.