Question

question
write an exponential function in the form $y = ab^x$ that goes through the points $(0, 16)$ and $(6, 1024)$.
answer attempt 1 out of 2
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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 $(6,1024)$

Substitute $a=16$, $x=6$, $y=1024$ into $y=ab^x$:
$1024 = 16b^6$

Step3: Isolate $b^6$

Divide both sides by 16:
$\frac{1024}{16} = b^6$
$64 = b^6$

Step4: Solve for $b$

Take the 6th root of both sides:
$b = \sqrt[6]{64} = 2$

Answer:

$y=16(2)^x$