Question

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write an exponential function for a graph that passes through the points (1,12) and (3, 192). write the function in the form y = a(b)^x.
+ - × ÷ 0/0 0^2 √0 ∛0 = ≠ < > ≤ ≥ (1) π
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Explanation:

Step1: Substitute (1,12) into formula

Substitute $x=1$, $y=12$ into $y=a(b)^x$:
$12 = a(b)^1 \implies 12 = ab$

Step2: Substitute (3,192) into formula

Substitute $x=3$, $y=192$ into $y=a(b)^x$:
$192 = a(b)^3$

Step3: Solve for $b^2$

Divide the second equation by the first:
$\frac{192}{12} = \frac{ab^3}{ab} \implies 16 = b^2$

Step4: Solve for positive $b$

Take positive square root (exponential base >0):
$b = \sqrt{16} = 4$

Step5: Solve for $a$

Substitute $b=4$ into $12=ab$:
$a = \frac{12}{4} = 3$

Step6: Write final function

Substitute $a=3$, $b=4$ into $y=a(b)^x$

Answer:

$y=3(4)^x$