Given the general exponential function:
[tex]f(x)=A\cdot b^x[/tex]Where A and b are parameters. Then, using the information provided in the problem:
[tex]\begin{gathered} f(3.5)=A\cdot b^{3.5}=12 \\ f(9)=A\cdot b^9=75 \end{gathered}[/tex]Taking the division:
[tex]\begin{gathered} \frac{A\cdot b^9}{A\cdot b^{3.5}}=\frac{75}{12} \\ b^{5.5}=6.25 \\ \Rightarrow b=1.39542 \end{gathered}[/tex]Now, we use f(9) = 75 to find the parameter A:
[tex]\begin{gathered} f(9)=A\cdot1.39542^9=75 \\ \Rightarrow A=3.7386 \end{gathered}[/tex]The function is:
[tex]f(x)=3.7386\cdot1.39542^x[/tex]We evaluate at x = 7.5:
[tex]\begin{gathered} f(7.5)=3.7386\cdot1.39542^{7.5} \\ \Rightarrow f(7.5)=45.50 \end{gathered}[/tex]