Answer:
Option b is correct.
The exponential function is, [tex] y=10.78 \cdot (0.7)^x[/tex]
Explanation:
Exponential Function:
An exponential fuction is [tex]f(x)=ab^x[/tex], ......[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,
[tex]10.78 = a \cdot b^0[/tex]
or
[tex]10.78 = a[/tex] or
∴ a = 10.78
Similarly, for point (1, 7.546)
we have; x = 1 and y = 7.546
[tex]7.546 = a \cdot b^1[/tex]
or
7.546 = ab or
ab = 7.546
Substitute the value of a = 10.78 in above equation to solve for b;
[tex]10.78 \cdot b = 7.546[/tex]
Divide both side by 10.78 we get
[tex]\frac{10.78}{10.78} \cdot b = \frac{7.546}{10.78}[/tex]
Simplify:
b = 0.7
Therefore, the exponential function for the given data is; [tex]y=10.78(0.7)^x[/tex]
