How do you find the exponential model y=ae^(bx) that goes through the points (0,4) and (5, 1/2)?

Jul 23, 2016

Solve for $a$ using equation 1 and then for $b$ using equation 2.

Explanation:

Basically we need to solve for both $a$ and $b$. Since $x = 0$ in the first equation I know that the exponent will be $0$ and anything raised to $0$ is evaluates to $1$ so let's do this first to easily solve for $a$.

$4 = a {e}^{b 0}$
4=a×1

Having the value of $a$ we use the second equation to solve for $b$.
$\frac{1}{2} = 4 {e}^{b 5}$
$\frac{1}{8} = {e}^{b 5}$
$\ln \left(\frac{1}{8}\right) = b 5$
$\ln \frac{\frac{1}{8}}{5} = b$