Question

equation.
lena
exponential regression results
$a = 527.237$
$b = 1.20174$
$\downarrow$
$y = 527.237(1.20174)^{12}$
$\downarrow$
$y = 4783.35$
megan
exponential regression results
$a = 21.248$
$b = 42.0283$
$c = 584.207$
$\downarrow$
$y = 21.248(12)^2 + 42.0283(12) + 584.207$
$\downarrow$
$y = 4148.26$
who solved the problem correctly? justify your reasoning.
\bigcirc neither lena nor megan solved the problem correctly. lena did not find a value for $c$ and megan rounded incorrectly.
\bigcirc neither lena nor megan solved the problem correctly. lena should have raised 527.237 to the $12^{th}$ and megan performed a quadratic regression.
\bigcirc lena solved the problem correctly by properly performing an exponential regression and substituting 12 in for $x$.
\bigcirc megan solved the problem correctly by properly performing an exponential regression and substituting 12 in for $x$.

Explanation:

An exponential regression follows the form $y = ab^x$, not a quadratic form $y=ax^2+bx+c$. Lena used the correct exponential regression structure, substituting $x=12$ properly into $y = 527.237(1.20174)^x$. Megan incorrectly used a quadratic regression formula instead of an exponential one, which does not match the required exponential regression task.

Answer:

Lena solved the problem correctly by properly performing an exponential regression and substituting 12 in for x.