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Given:
An exponential function goes through points (0, 14) and (4, 8750).
To find:
The function.
Solution:
The general form of an exponential function is
[tex]y=ab^x[/tex] ...(i)
It goes through points (0, 14) and (4, 8750). It means the the equation must be satisfied by these points.
Putting x=0 and y=14 in (i), we get
[tex]14=ab^0[/tex]
[tex]14=a[/tex]
The value of a is 14.
Putting a=14, x=4 and y=8750 in (i), we get
[tex]8750=14b^{4}[/tex]
[tex]\dfrac{8750}{14}=b^{4}[/tex]
[tex]625=b^{4}[/tex]
It can be written as
[tex]5^4=b^{4}[/tex]
[tex]5=b[/tex]
The value of b is 5.
Putting a=14 and b=5 in (i), we get
[tex]y=14b^5[/tex]
Therefore, the required exponential function is [tex]y=14b^5[/tex].