Question

question
write an exponential function in the form $y = ab^x$ that goes through the points $(0, 13)$ and $(8, 3328)$.
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Explanation:

Step1: Solve for $a$ using $(0,13)$

Substitute $x=0, y=13$ into $y=ab^x$:
$13 = ab^0$
Since $b^0=1$, we get $a=13$.

Step2: Substitute $a$ and $(8,3328)$

Substitute $a=13$, $x=8$, $y=3328$ into $y=ab^x$:
$3328 = 13b^8$

Step3: Isolate $b^8$

Divide both sides by 13:
$\frac{3328}{13}=b^8$
$256 = b^8$

Step4: Solve for $b$

Take the 8th root of both sides:
$b = \sqrt[8]{256}$
Since $2^8=256$, $b=2$.

Answer:

$y=13(2)^x$