Question

Explain why the initial value of any function of the form f(x) = a(bx) is equal to a.

Answer 1

We are given the function of the
`f(x) = ab^x`.

Now, we know,

The initial value of the function will be obtained when x= 0.

So, substituting x= 0 in the function, we get,

`f(0) = ab^0`

As, 'If any number has the power equal to 0, the resultant is the 1 i.e.
`x^(0)=1`

So, we ger,

`f(0) = ab^0` implies
`f(0) = a* 1` i.e. f(0)= a i.e. The initial value is equal to 'a'.

Answer 2

When you substitute 0 for the exponent x, the expression simplifies to a times 1, which is just a. This is because any number to the 0 power equals 1. Since the initial value is the value of the function for an input of 0, the initial value for any function of this form will always be the value of a.