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

It's B, just took the quiz :)

Option b is correct.

The exponential function is,

Explanation:

Exponential Function:

An exponential fuction is  , ......[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,  

or

or

∴ a = 10.78

Similarly, for point (1, 7.546)

we have; x = 1 and y = 7.546

or

7.546 = ab   or

ab = 7.546

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

Divide both side by 10.78 we get

Simplify:

b = 0.7

Therefore, the exponential function for the given data is;  

43

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