Question

question
write an exponential function in the form $y = ab^x$ that goes through the points $(0, 16)$ and $(5, 512)$.

Explanation:

Step1: Solve for $a$ using $(0,16)$

Substitute $x=0, y=16$ into $y=ab^x$:
$16 = ab^0$
Since $b^0=1$, we get $a=16$.

Step2: Substitute $a$ and $(5,512)$

Substitute $a=16$, $x=5, y=512$ into $y=ab^x$:
$512 = 16b^5$

Step3: Isolate $b^5$

Divide both sides by 16:
$\frac{512}{16} = b^5$
$32 = b^5$

Step4: Solve for $b$

Take 5th root of both sides:
$b = \sqrt[5]{32} = 2$

Answer:

$y=16(2)^x$