We have been taught that linear functions, usually expressed in the form y=mx+b, when given a input of 0,1,2,3, etc..., you can get from one output to the next by adding some constant (in this case, 1). Input 0 1 2 Output 1 2 3 But with exponential functions (which are usually expressed in the form y=a⋅*b^x), instead of adding a constant, you multiply by a constant. (In this case, 2) Input 0 1 2 3 Output 1 2 4 8 We can keep going, can't we? Input 0 1 2 3 4 Output 1 2 4 16 256

Tessa Peters

Tessa Peters

Answered question

2022-10-27

We have been taught that linear functions, usually expressed in the form y=mx+b, when given a input of 0,1,2,3, etc..., you can get from one output to the next by adding some constant (in this case, 1).
Input Output 0 1 1 2 2 3
But with exponential functions (which are usually expressed in the form y = a b x ), instead of adding a constant, you multiply by a constant. (In this case, 2)
Input Output 0 1 1 2 2 4 3 8
We can keep going, can't we?
Input Output 0 1 1 2 2 4 3 16 4 256

Answer & Explanation

HadoHaurrysap3w

HadoHaurrysap3w

Beginner2022-10-28Added 10 answers

Each of your tables is found by taking 2 to the power of the previous table (possibly with a shift by 1). As the formula for your second table is 2 x , the formula for your third table is 2 2 x 1 (for x 1).
Cale Terrell

Cale Terrell

Beginner2022-10-29Added 3 answers

Note that your table can be written as
Input Output 1 2 2 1 1 2 2 2 2 1 3 2 2 3 1 4 2 2 4 1
Tetration is the operation you could say that succeeds exponentiation. As an example, notationally, if we want to represent "a to the a to the a to the a"th power, we use
4 a = a a a a

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