Question

I’m confused on how to do this please help me walk through on how to solve this :(

Answer 1

Given:

Power function and point is

Points

`\begin{gathered} (1,4) \\ (5,41)^ \end{gathered}`

Find-:

Power of function

Explanation-:

Let the power function is:

`f(x)=ax^n`

Check for points (1,4)

`\begin{gathered} f(x)=ax^n \\ \\ (x,f(x))=(1,4) \\ \\ 4=a(1)^n \\ \\ a=4..................(1) \end{gathered}`

Check for points (5,41)

`\begin{gathered} f(x)=ax^n \\ \\ f(x)=4x^n \\ \\ (x,f(x))=(5,41) \end{gathered}`

Put the value then,

`\begin{gathered} f(x)=4x^n \\ \\ 41=4(5)^n \\ \\ (41)/(4)=5^n \\ \\ 10.25=5^n \end{gathered}`

Taking log both sides then

`\begin{gathered} 10.25=5^n \\ \\ \ln(10.25)=\ln5^n \\ \\ \ln(10.25)=n\ln5 \\ \\ 2.327=n*1.609 \\ \\ n=(2.327)/(1.609) \\ \\ n=1.446 \end{gathered}`

So the function is:

`\begin{gathered} y=ax^n \\ \\ y=4x^(1.446) \end{gathered}`