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

Answer:

$f(x) = 4 \times (\dfrac{1}{8})^{x}$.

Step-by-step explanation:

Let $f(x) = a \cdot b^{x}$ represent this exponential function. $a \ne 0$, $b > 0$.

$b^{0} = 1$. As a result, $a = f(0) = 4$.

$a \cdot b = 4 \cdot b = f(1) = \dfrac{1}{2}$.

As a result,

$b = \dfrac{1}{8}$.

$f(x) = a \cdot b^{x} = 4 \times (\dfrac{1}{8})^{x}$.

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