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=(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=(8)/(b^3)...............(2) \end{gathered}`

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

`\begin{gathered} (5)/(b^2)=(8)/(b^3) \\ \\ (b^3)/(b^2)=(8)/(5) \\ \\ b=(8)/(5) \\ \\ b=1.6 \end{gathered}`

So the value of "a" is:

`\begin{gathered} a=(8)/(b^3) \\ \\ a=(8)/((1.6)^3) \\ \\ a=(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}`