Answer :
The exponential function passing through (0,15) and (3,3240) is [tex]y=15\times 6^x[/tex].
What is Exponential Function?
An exponential function is one with the mathematical formula f (x) = axe, where "x" is a variable and "a" is a constant that serves as the function's basis and must be greater than 0. The graph of exponential function is curve that goes to infinite. The value of dependent variable increases exponentially when the value of independent variable increases.
The standard form of exponential function is [tex]y=ab^x[/tex].
Putting (0,15) in place of x and y, we get
[tex]y=ab^x\\15=ab^0\\a=15[/tex]
Now, putting (3,3240) in the function, we get
[tex]3240=15\times b^3\\b^3=216\\b = 6[/tex]
So, the exponential function is [tex]y=15\times 6^x[/tex].
Therefore, the exponential function is [tex]y=15\times 6^x[/tex].
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