Respuesta :
The general form of an exponential function is:
[tex]y=a\cdot b^x^{}[/tex]where a ≠ 0, b > 0 and b ≠ 1
f(-1) = 26 and f(6.5) = 14, that is,
[tex]\begin{gathered} 26=a\cdot b^{-1} \\ 26=\frac{a}{b} \\ 26\cdot b=a \end{gathered}[/tex][tex]\begin{gathered} 14=a\cdot b^{6.5} \\ 14=26\cdot b\cdot b^{6.5} \\ 14=26\cdot b^{7.5} \\ \frac{14}{26}=b^{7.5} \\ \ln (\frac{14}{26})=7.5\cdot\ln b \\ -\frac{0.619}{7.5}=\ln b \\ e^{-0.0825}=b \\ 0.92=b \end{gathered}[/tex]Then,
[tex]\begin{gathered} a=26\cdot b \\ a=26\cdot0.92 \\ a=23.92 \end{gathered}[/tex]Finally, the function is:
[tex]y=23.92\cdot0.92^x^{}[/tex]