Question

Why is the growth factor +1 plus r for an exponential growth function?

Answer 1

The exponential growth model is given by this general expression:

`y = a (1+r)^t`

And the exponential model decay model is given by:

`y = a (1-r)^t`

Where a the initial amount r the growth factor of rate anf t the time.

The reason with we need to add 1+r in the base of the model is because each period of time
`t_1` we have an increase of the initial amount by a factor of (1+r) so after n periods we will have (1+r)^n times the initial amount.

Explanation:

In general an exponential model is given by this formula:

`y = a(b)^x`

Where:

a = the constant, b = the base and x x the exponent.

The exponential growth model is given by this general expression:

`y = a (1+r)^t`

And the exponential model decay model is given by:

`y = a (1-r)^t`

Where a the initial amount r the growth factor of rate anf t the time.

The reason with we need to add 1+r in the base of the model is because each period of time
`t_1` we have an increase of the initial amount by a factor of (1+r) so after n periods we will have (1+r)^n times the initial amount.