Question

Explain why the initial value of any function of the form f(x) = a(b^x) is equal to a. no sample response

Answer 1

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

Step-by-step explanation:

The initial value of any function of the form f(x) = a(bˣ) is equal to a. In this equation, a represents the initial value or the value of the function when x = 0. The base b represents the rate at which the function grows or decays. When x = 0, the exponent is zero, and any number raised to the power of zero is equal to one. So, a(b⁰) simplifies to a(1), which is equal to a.

Answer 2

Basically, it is a because the b elevated to the zero results in 1, which multiplies a. Then the initial value is a.

Step-by-step explanation:

The initial value of a function f(x) is f(0), that is, the value of f when x = 0.

Format:

`f(x) = ab^(x)`

The initial value is f(0). So

`f(x) = ab^(x)`

`f(0) = ab^(0)`

Any non-zero value elevated to the zero is 1.

So

`f(0) = ab^(0) = a*1 = a`

Basically, it is a because the b elevated to the zero results in 1, which multiplies a. Then the initial value is a.