1) A grandmother proposes two savings plans for a newborn grandchild, one depositing €1000 initially plus €100 extra each year, the other depositing €1 initially and doubling the amount each year. 2) A table shows the amounts accumulated under each plan at different ages. 3) Plan 1's function is f(x) = 1000 + 100x, while Plan 2's function is f(x) = 2^x. 4) The conclusion is that Plan 2 becomes more favorable than Plan 1 starting at age 11.

1. Exponent functions
Interesting Mathematics 5

2. At your birth, your grandmother proposes two
plans for you to deposit annually a certain amount
of money:
1. At birth and on each birthday €1000, with
additionally on each anniversary €100 extra.
2. At birth €1 and at every birthday, your
grandmother doubles this amount.
What do you choose?
Set a relationship f(x) for the amount of money you
receive when you become x years old.

3. Age (years) Plan 1: amount in € Plan 2: amount in €
0 1000 1
1 1100 2
2
3
4
5
6
7
8
9
10
11
12
13
14

4. Age (years) Plan 1: amount in € Plan 2: amount in €
0 1000 1
1 1100 2
2 1200 4
3 1300 8
4 1400 16
5 1500 32
6 1600 64
7 1700 128
8 1800 256
9 1900 512
10 2000 1024
11 2100 2048
12 2200 4096
13 2300 8192
14 2400 16384

5. Plan 1:
Plan 2:
( ) 2x
f x 
( ) 1000 .100f x x 

6. Conclusion:
From the age of eleven, savings
plan 2 is the more favourable one.