Question

The table of values below represent an exponential function. Write an exponential equation that models the data

Answer 1

It's B, just took the quiz :)

Answer 2

Option b is correct.

The exponential function is,
`y=10.78 \cdot (0.7)^x`

Explanation:

Exponential Function:

An exponential fuction is
`f(x)=ab^x`, ......[1] ; where a≠0 and b is the base with b>1 and x is any real number.

Consider any two points from the given table (0, 10.78) and (1, 7.546).

To find the value of a and b by substituting these points in equation [1];

For point (0, 10.78)

we have,

x = 0 and b = 10.78

then,

`10.78 = a \cdot b^0`

or

`10.78 = a` or

∴ a = 10.78

Similarly, for point (1, 7.546)

we have; x = 1 and y = 7.546

`7.546 = a \cdot b^1`

or

7.546 = ab or

ab = 7.546

Substitute the value of a = 10.78 in above equation to solve for b;

`10.78 \cdot b = 7.546`

Divide both side by 10.78 we get

`(10.78)/(10.78) \cdot b = (7.546)/(10.78)`

Simplify:

b = 0.7

Therefore, the exponential function for the given data is;
`y=10.78(0.7)^x`