Question

The graph of an exponential function passed through (0,4) and (1,1/2) write the rule for the function and tell whether the graph represents exponential growth or exponential decay

Answer 1

`f(x) = 4 * ((1)/(8))^(x)`.

Explanation:

Let
`f(x) = a \cdot b^(x)` represent this exponential function.
`a \\e 0`,
`b > 0`.

`b^(0) = 1`. As a result,
`a = f(0) = 4`.

`a \cdot b = 4 \cdot b = f(1) = (1)/(2)`.

As a result,

`b = (1)/(8)`.

`f(x) = a \cdot b^(x) = 4 * ((1)/(8))^(x)`.

This function represents an exponential decay since
`0 < b < 1`.