Question

Find the equation of the exponential function represented by the table below: 2 y 0 0.01 1 0.005 2 0.0025 3 0.00125 a Answer: Y Submit Answer

Answer 1

Concept:

The general form of an exponential function is given below as

`y=ab^x`

Step 1:

when x=0, y=0.01

`\begin{gathered} y=ab^x \\ 0.01=ab^0 \\ a=0.01 \end{gathered}`

Step 2:

When x=1, y=0.005

`\begin{gathered} y=ab^x \\ 0.005=0.01b^1 \\ 0.005=0.01b \\ divide\text{ both sides by 0.01} \\ (0.01b)/(0.01)=(0.005)/(0.01) \\ b=(1)/(2) \end{gathered}`

Hence,

The exponential equation will be

`\begin{gathered} \Rightarrow y=0.01((1)/(2))^x \\ \Rightarrow y=0.01(0.5)^x \end{gathered}`