Given:
The table of values.
To find:
The equation of the exponential function represented by the table.
Solution:
The general form of an exponential function is
...(i)
where, a is initial value and b is growth factor.
From the given table it is clear that the function passes through (0,3) and (1,1.5). So, the must be satisfy by these points.
Putting x=0 and y=3 in (i), we get
![3=ab^0](/tpl/images/1002/5742/8e29a.png)
![3=a(1)](/tpl/images/1002/5742/35763.png)
![3=a](/tpl/images/1002/5742/29390.png)
Putting a=3, x=1 and y=1.5 in (i), we get
![1.5=3b^1](/tpl/images/1002/5742/d66e9.png)
![\dfrac{1.5}{3}=b](/tpl/images/1002/5742/b37d7.png)
![\dfrac{1}{2}=b](/tpl/images/1002/5742/7da77.png)
Putting
and
in (i), we get
![y=3\left(\dfrac{1}{2}\right)^x](/tpl/images/1002/5742/8623f.png)
Therefore, the required equation for exponential function is
.