Question

How do I solve this problem? What are the steps?

Find a possible exponential function in y=a(b^x) form that represents each situation described below. Your answer should look like y=a(b)^x. Has an initial value of 2 and passes through the point (3,128)

Answer 1

`y=2(4)^x`

Explanation:

The equation `y = ab^x` describes an exponential function, where `a` is the initial value and `b` is the rate of growth or decay.

We're told that the initial value is `2`, so `a=2`.

`y=2(b)^x`

We are also given the point `(3,128)`. Substitute `3` for `x` and `128` for `y`.

`128=2(b)^3`

Now, solve for `b`.

`128=2(b)^3`
`64=b^3`
`b = root(3) 64`
`b=4`

Thus, the equation is `y=2(4)^x`.