Question

On your fifteenth birthday you discover you have a rich aunt sally aunt sally is a very generous women and wants to provide for your future she has decided that she will initially give you $1 then $2 the next year and so on doubling the amount each year until your 30. Use a chart to keep track how much money she will give you each year for the first 5 years.

Answer 1

Let's fill a table with the first two years, we already know those

So, we need to complete the chart for years 3,4, and 5. We know that in year 3, will receive double the money than we get in year 2, this is 2*$2=$4. Now we write that result on our table.

In year 4 we'll get double the money than in year 3, this is 2*$4=$8

Similarly, in year 5 we get double the money than what we got in year 4: 2*$8=$16

And we have filled in the table!

Now, a bonus, the pattern here seems to be an equation, notice this:

year 1 -> $1 = $2^0

year 2 ->$2 = $2^1

year 3 -> $4 = $2^2

year 4 -> $8 = $2^3

year 5 -> $16 = $2^4

This means that the amount of money we'll receive each year is given by

`2^(t-1)`

Where t is the year! (year 1, year 2, etc)