Question

The graph of an exponential function is given. Which of the following is the correct equation of the function? (5 points)

Answer 1

Option 1.
`y = 3.5 ^ x`

Explanation:

Exponential functions usually have the following form:

`y = b(a) ^ x`

Where a and b are real numbers.

b is the coefficient and a is the base. The variable x is the exponent.

In all the options shown, the coefficient is b = 1.

Since the graph of the function has a value close to 10 when x = 2. Then we can discard the options in which the basis of the function is less than 1.

Then we have two options left:

`1) y = 3.5 ^ x\\\\3) y = 2.4 ^ x`

When
`x = 2\ ,\ 2.4 ^ x = 5.76`

When
`x = 2\ \ ,\ 3.5 ^ x = 12.25`

Notice in the graph that function 3) is greater than 6 when x = 2, while function 1) is close to 12 when x = 2.

Therefore the correct option is the first option.

`y = 3.5 ^ x`