Question

consider the function $y = f(x)$ graphed below. the two points marked on the graph are $a = (0,2)$ and $b = (3,16)$. give a possible formula, of the form $ca^x$, for the function graphed. $y = $

Explanation:

Step1: Find C using point A(0,2)

Substitute $x=0$, $y=2$ into $y=Ca^x$:
$2 = Ca^0$
Since $a^0=1$ for $a
eq0$, we get $C=2$.

Step2: Find a using point B(3,16)

Substitute $C=2$, $x=3$, $y=16$ into $y=Ca^x$:
$16 = 2a^3$
Divide both sides by 2: $a^3 = 8$
Take cube root: $a = \sqrt[3]{8}=2$

Step3: Write the final formula

Substitute $C=2$ and $a=2$ into $y=Ca^x$.

Answer:

$y=2\cdot2^x$ (or $y=2^{x+1}$)