Question

which of these best represents the output value for an exponential function with an initial value of 1.2, a base of 10, where the input value is 4?
○ $1.2 \cdot 1.2 \cdot 1.2 \cdot 1.2 \cdot 10$
○ $1.2 \cdot 10 \cdot 4$
○ $1.2 \cdot 10 \cdot 10 \cdot 10 \cdot 10$
○ $1.2 + 10 \cdot 10 \cdot 10 \cdot 10$

Explanation:

Step1: Recall exponential function form

The general form of an exponential function is $f(x) = a \cdot b^x$, where $a$ is the initial value, $b$ is the base, and $x$ is the input value.

Step2: Substitute given values

Here, $a=1.2$, $b=10$, $x=4$. Substitute into the formula: $f(4) = 1.2 \cdot 10^4$.

Step3: Expand the exponential term

$10^4$ is equivalent to $10 \cdot 10 \cdot 10 \cdot 10$, so $f(4) = 1.2 \cdot 10 \cdot 10 \cdot 10 \cdot 10$.

Answer:

1.2 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10