Question

Model the data using an exponential function f(x) = Abx. HINT [See Example 1.]

Answer 1

We take the function as a sequence

Term 1 ⇒ 5 
Term 2 ⇒ 4
Term 3 ⇒ 3.2

Between terms, there is a common ratio of ⁴/₅
We get it from here:
Term 2 / Term 1 = $\frac{4}{5}$
Term 3 / Term 2 = $\frac{3.2}{4}$ = $\frac{4}{5}$

When a sequence has a common ratio between term, the sequence is a Geometric Sequence

$n_{th}term=ar^{n-1}$
Where $a$ is the first term, $r$ is the common ratio, and $n$ is the term number

We have: $a=5$ and $r= \frac{4}{5}$
The formula for the function is

$f(x)=5( \frac{4}{5})^{x-1}$