Question

Write the equation in exponential form using the two points (0,1) and (1,3)

Answer 1

`y=3^x`

Explanation:

The equation of the function in exponential form is

`y=a\cdot b^x`

The function is determined using points (0,1) and (1,3), so their coordinates satisfy the eduation. Substitute them:

`1=a\cdot b^0\Rightarrow a=1\ \ [b^0=1]\\ \\3=a\cdot b^1\Rightarrow 1\cdot b=3,\ b=3`

Thus, the equation of the function is

`y=3^x`