Question

I need help number 5

Answer 1

A exponential function is given by:

$y=ab^x$

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:

$\begin{gathered} (-2,1.91) \\ 1.91=ab^{-2}_{\text{ }}(1) \\ ------- \\ (-1,2.1) \\ 2.1=ab^{-1}_{\text{ }}(2) \end{gathered}$

From (2) solve for b:

$b=\frac{a}{2.1}_{\text{ }}(3)$

Replace (3) into (1):

$\begin{gathered} 1.91=\frac{a}{b^2} \\ 1.91b^2=a \\ 1.91(\frac{a}{2.1})^2=a \\ \frac{191}{441}a^2=a \\ \frac{191}{441}a=1 \\ a=\frac{441}{191} \\ \end{gathered}$

Replace a into (3):

$\begin{gathered} b=\frac{210}{191} \\ \end{gathered}$

a.

b = 210/191

b.

$\frac{210}{191}-1=0.09948$

c.

$a=\frac{441}{191}$

d.

$f(x)=\frac{441}{191}\cdot(\frac{210}{191})^x$