Respuesta :

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]

ACCESS MORE
EDU ACCESS