The given function is
[tex]f(x) = a e^{kx}[/tex]
And it is given that [tex]f(4)=12[/tex]
On using this information, we will get
[tex]12 = a e^{4k}[/tex]
And the other point is [tex]f(7)=5[/tex]
Using this point, we will get
[tex]5= ae^{7k}[/tex]
Dividing both equations, we will get
[tex]\frac{12}{5} = e^{4k-7k}[/tex]
Taking ln to both sides
[tex]ln( \frac{12}{5} ) = -3k[/tex]
[tex]k = -0.29[/tex]
Performing back substitution ,
[tex]12 = a e^{-0.29*4}
\\
a =38.28[/tex]
