Given:
An exponential function goes through points (0,6) and (5, 6144).
To find:
The exponential function.
Solution:
The general form of an exponential function is
[tex]y=ab^x[/tex] ...(i)
It goes through points (0,6) and (5, 6144). It means the equation must be satisfied by these two points.
Putting x=0 and y=6, we get
[tex]6=ab^0[/tex]
[tex]6=a[/tex]
Putting a=6, x=5 and y=6144, we get
[tex]6144=6b^5[/tex]
[tex]\dfrac{6144}{6}=b^5[/tex]
[tex]1024=b^5[/tex]
Taking 5th root on both sides, we get
[tex]\sqrt[5]{1024}=b[/tex]
[tex]4=b[/tex]
Putting a=6 and b=4, we get
[tex]y=6(4)^x[/tex]
Therefore, the required exponential function is [tex]y=6(4)^x[/tex].
