Question

write an exponential function in the form $y = ab^x$ that goes through the points $(0, 15)$ and $(2, 1215)$. answer attempt 1 out of 2 submit answer

Explanation:

Step1: Find $a$ using $(0,15)$

Substitute $x=0$, $y=15$ into $y=ab^x$:
$15 = ab^0$
Since $b^0=1$, we get $a=15$.

Step2: Find $b$ using $(2,1215)$

Substitute $a=15$, $x=2$, $y=1215$ into $y=ab^x$:
$1215 = 15b^2$
First, solve for $b^2$:
$b^2 = \frac{1215}{15} = 81$
Take the positive root (standard for exponential growth):
$b = \sqrt{81} = 9$

Step3: Build the function

Substitute $a=15$ and $b=9$ into $y=ab^x$.

Answer:

$y=15(9)^x$