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Find the equation of the exponential function represented by the table below:

Find The Equation Of The Exponential Function Represented By The Table Below class=

Sagot :

sophiew4

Answer:

[tex]f(x)=5(4)^x[/tex]

Step-by-step explanation:

The exponential function is [tex]f(x)=ab^x[/tex].  [tex]a[/tex] is the initial value of the function, or the y-value when x=0. In this case, [tex]a[/tex]=5. If we enter that into the equation:

[tex]f(x)=5b^x[/tex]

Then we can use another point to solve for [tex]b[/tex].

[tex]20=5b^1[/tex]

Since anything raised to the power of 1 remains the same, we can continue to solve algebraically.

[tex]20=5b\\\frac{20}{5}=\frac{5b}{5}\\b=4[/tex]

Now that we have both the [tex]a[/tex] and [tex]b[/tex] value, we can return to the exponential function and fill in the blanks.

[tex]f(x)=5(4)^x[/tex]

I hope this helps!

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