Question

question
write an exponential function in the form $y = ab^x$ that goes through the points $(0, 11)$ and $(3, 2376)$.

Explanation:

Step1: Find $a$ using $(0,11)$

Substitute $x=0, y=11$ into $y=ab^x$:
$11 = ab^0$
Since $b^0=1$, we get $a=11$.

Step2: Substitute $a$ and $(3,2376)$

Substitute $a=11$, $x=3, y=2376$ into $y=ab^x$:
$2376 = 11b^3$

Step3: Solve for $b$

First, divide both sides by 11:
$\frac{2376}{11} = b^3$
$216 = b^3$
Take the cube root of both sides:
$b = \sqrt[3]{216} = 6$

Step4: Write the final function

Substitute $a=11$ and $b=6$ into $y=ab^x$.

Answer:

$y=11(6)^x$