Describe the pattern 0.7, 2.1, 6.3, 18.9

You multiply 3 by each number.

0.7•3=2.1

2.1•3=6.3 etc ...

This pattern would be exponential.

Lets look at it.

0.7 x 3 = 2.1

2.1 x 3 = 6.3

6.3 x 3 = 18.9

The first term 0.7 is essentially 0.7 x zero 3's (0.7)

The second term is 0.7 x one 3 (0.7 x 3)

The third term is 0.7 x two 3's (0.7 x 3 x 3)

The fourth term is 0.7 x three 3's (0.7 x 3 x 3 x 3)

We can write a mathematical equation to describe this pattern:

f (x) = 0.7 (3) ^ (x-1)

Lets see if this actually gives us the right values.

First term: x = 1

Second term: x = 2

Third term: x = 3

Fourth term:x = 4

First term: f (1) = 0.7 (3) ^ (1-1) = 0.7 (3) ^0 = 0.7 (3^0 simply becomes 1)

Second term: f (2) = 0.7 (3) ^ (2-1) = 0.7 (2) ^1 = 0.7 x 3 = 2.1

Third term: f (3) = 0.7 (3) ^ (3-1) = 0.7 (3) ^2 = 0.7 x 3 x 3 = 6.3

Fourth term: f (4) = 0.7 (3) ^ (4-1) = 0.7 (3) ^3 = 0.7 x 3 x 3 x 3 = 18.9

As you can see, this function outputs the same values in the pattern.

This function, f (x) = 0.7 (3) ^ (x-1), is indeed an exponential function, so the pattern formed by this function is an exponential pattern.