Question

(Q8) The graph of an exponential function is given. Which of the following is the correct equation of the function? (Picture Provided)

Answer 1

b.
`y=3.9^x`

Explanation:

Remember that the standard exponential function is
`y=ab^x`

where

`a` is the coefficient

`b` is the base

If
`b>0`, the function is growing

If
`0<b<1` the graph is decaying

We can infer from the graph that the function is growing, so we can discard
`y=0.45^x` and
`y=0.73^x`.

Now, to evaluate our tow remaining equations, we are using the test values
`x=0` and
`x=1`:

For
`y=1.8^x`

For
`x=0`

`y=1.8^0`

`y=0`

For
`x=1`

`y=1.8^1`

`y=1.8`

The graph passes through the points (0,1) and (1, 1.8)

For
`y=3.9^x`

`x=0`

`y=3.9^0`

`y=0`

`x=1`

`y=3.9^1`

`y=3.9`

The graph passes through the points (0,1) and (1, 3.9)

We can see in the graph when
`x=1`,
`y` is almost 4, so we can conclude that the correct equation is
`y=3.9^x`