Question

A 2-column table has 5 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2. The second column is labeled f (x) with entries one-eighth, one-fourth, one-half, 1, 2. What is the initial value of the exponential function represented by the table? One-eighth One-fourth One-half 1

Answer 1

1/2 is correct

Explanation:

Answer 2

Initial value is
`(1)/(2)`.

Explanation:

Let us assume that the exponential function is
`f(x) = a(b)^(x)` ...... (1)

Now, the point
`(0,(1)/(2))` will satisfy the above equation.

Now, this point on the graph of the exponential function will be sufficient to find the initial value of the function (1) i.e. a.

Now, putting the value x = 0 and
`y = (1)/(2)` in the equation (1) we get,
`f(x) = a(b)^(x)`

⇒
`(1)/(2) = a(b)^(0) = a`

⇒
`a = (1)/(2)` (Answer)