Question

write an exponential function in the form $y = ab^x$ that goes through the points $(0, 3)$ and $(2, 243)$. answer attempt 1 out of 2 submit answer

Explanation:

Step1: Solve for $a$ using $(0,3)$

Substitute $x=0$, $y=3$ into $y=ab^x$:
$3 = ab^0$
Since $b^0=1$, we get $a=3$.

Step2: Solve for $b$ using $(2,243)$

Substitute $a=3$, $x=2$, $y=243$ into $y=ab^x$:
$243 = 3b^2$
Divide both sides by 3: $\frac{243}{3}=b^2$ → $81 = b^2$
Take positive root (exponential base >0): $b = \sqrt{81}=9$

Step3: Build the final function

Substitute $a=3$, $b=9$ into $y=ab^x$.

Answer:

$y=3\cdot9^x$