Question

write an exponential function in the form $y = ab^x$ that goes through the points $(0, 13)$ and $(3, 4459)$. answer attempt 1 out of 2

Explanation:

Step1: Find $a$ 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 $(3,4459)$

Substitute $a=13$, $x=3, y=4459$ into $y=ab^x$:
$4459 = 13b^3$

Step3: Solve for $b$

First, divide both sides by 13:
$\frac{4459}{13} = b^3$
$343 = b^3$
Take cube root of both sides:
$b = \sqrt[3]{343} = 7$

Step4: Write the final function

Substitute $a=13$ and $b=7$ into $y=ab^x$.

Answer:

$y=13(7)^x$