A exponential function is given by:
[tex]y=ab^x[/tex]y represents the output.
a represents the initial value of the function.
b represents the rate of growth.
x represents the input.
Using the given points:
[tex]\begin{gathered} (-2,1.91) \\ 1.91=ab^{-2}_{\text{ }}(1) \\ ------- \\ (-1,2.1) \\ 2.1=ab^{-1}_{\text{ }}(2) \end{gathered}[/tex]From (2) solve for b:
[tex]b=\frac{a}{2.1}_{\text{ }}(3)[/tex]Replace (3) into (1):
[tex]\begin{gathered} 1.91=\frac{a}{b^2} \\ 1.91b^2=a \\ 1.91(\frac{a}{2.1})^2=a \\ \frac{191}{441}a^2=a \\ \frac{191}{441}a=1 \\ a=\frac{441}{191} \\ \end{gathered}[/tex]Replace a into (3):
[tex]\begin{gathered} b=\frac{210}{191} \\ \end{gathered}[/tex]a.
b = 210/191
b.
[tex]\frac{210}{191}-1=0.09948[/tex]c.
[tex]a=\frac{441}{191}[/tex]d.
[tex]f(x)=\frac{441}{191}\cdot(\frac{210}{191})^x[/tex]