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!
