Question

A function f is given by the formula f(x)=a⋅ekx for constants a and k. we also know that f(4)=12 and f(7)=5. find numerical values for the constants a and k.

Answer 1

The given function is

$f(x) = a e^{kx}$

And it is given that $f(4)=12$

On using this information, we will get

$12 = a e^{4k}$

And the other point is $f(7)=5$

Using this point, we will get

$5= ae^{7k}$

Dividing both equations, we will get

$\frac{12}{5} = e^{4k-7k}$

Taking ln to both sides

$ln( \frac{12}{5} ) = -3k$

$k = -0.29$

Performing back substitution ,

$12 = a e^{-0.29*4} \\ a =38.28$