Question

Consider the scatter plot.Curve of best fit: f(x)= ____ (____)^x Options: For the first blank 1.89 or 1.35.Second Blank: 0.11, 1.89, 0.65,1.35

Answer 1

Given:

The point of the graph

(2,5), (3,8)

Find-:

The equation of the graph

Explanation-:

Let the equation is:

$f(x)=a(b)^x$

Give points are,

$\begin{gathered} (x,y)=(2,5) \\ \\ (x,y)=(3,8) \end{gathered}$

If the point on the graph then the equation specified the graph then,

$\begin{gathered} y=a(b)^x \\ \\ (x,y)=(2,5) \\ \\ 5=a(b)^2 \\ \\ a=\frac{5}{b^2}............(1) \end{gathered}$

For the second point

$\begin{gathered} y=a(b)^x \\ \\ (x,y)=(3,8) \\ \\ 8=a(b)^3 \\ \\ a=\frac{8}{b^3}...............(2) \end{gathered}$

From eq(1) and eq(2), value of "a" is equal then,

$\begin{gathered} \frac{5}{b^2}=\frac{8}{b^3} \\ \\ \frac{b^3}{b^2}=\frac{8}{5} \\ \\ b=\frac{8}{5} \\ \\ b=1.6 \end{gathered}$

So the value of "a" is:

$\begin{gathered} a=\frac{8}{b^3} \\ \\ a=\frac{8}{(1.6)^3} \\ \\ a=\frac{8}{4.096} \\ \\ a=1.95312 \end{gathered}$

So the equation becomes,

$\begin{gathered} f(x)=a(b)^x \\ \\ f(x)=1.95312(1.6)^x \end{gathered}$