Question

This one is super hard

Answer 1

We use the first point given (0, 14) to solve a in terms of b. We have

$\begin{gathered} 14=ab^0 \\ 14=a \end{gathered}$

We use the second point given (3,3024) to solve for the value of b,

$3024=ab^3$

Substitute the value of a solved by the equation above on the equation above and solve

$\begin{gathered} 3024=14b^3 \\ b=\sqrt[3]{216} \\ b=6 \end{gathered}$

Hence, the exponential function is written as

$f(x)=14(6)^x$