Question

B. I Find the equation of the exponential function represented by the table below: y The equation would be y = 1.2% 0 1 +2. 1

Answer 1

exponential formula:

`y=a\cdot b^x`

where a and b are two constants.

Replacing with x = 0, and y = 1, we get:

`\begin{gathered} 1=a\cdot b^0 \\ 1=a \end{gathered}`

Replacing with a = 1, x = 1, and y = 3, we get:

`\begin{gathered} 3=1\cdot b^1 \\ 3=b \end{gathered}`

Then, the equation is:

`y=1\cdot3^x`

This result can be checked with the other points of the table.

When x = 2,

`y=1\cdot3^2=9`

When x = 3,

`y=1\cdot3^3=27`