Question 1137506
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The general template for an exponential function is 
{{{y = a*b^x}}}
where 'a' and 'b' are fixed values (constants).


The first point given to us is (0,6) meaning that x = 0 and y = 6 pair up together. Let's plug them both into the template to see what happens
{{{y = a*b^x}}}


{{{6 = a*b^0}}} replace x with 0; replace y with 6


{{{6 = a*1}}} anything to the zeroth power is equal to 1


{{{6 = a}}} one times any number is itself


{{{a = 6}}} So we have one of the constants we need.


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Now plug in the other point (x,y) = (3,750). Also we will plug in a = 6 that we found earlier. Then solve for b


{{{y = a*b^x}}}


{{{y = 6*b^x}}} replace 'a' with 6


{{{750 = 6*b^3}}} plug in (x,y) = (3,750)


{{{750/6 = (6*b^3)/6}}} Divide both sides by 6


{{{125 = b^3}}}


{{{b^3 = 125}}}


{{{root(3,b^3) = root(3,125)}}} Apply the cube root to both sides. You can also think of it as raising both sides to the 1/3 power. 


{{{b = 5}}} We found the other constant


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Therefore, 
a = 6
b = 5


Making the function be {{{f(x) = 6(5)^x}}} which is the same as {{{y = 6(5)^x}}} since y = f(x).


As a check, plug in x = 0 to get
{{{f(x) = 6(5)^x}}}
{{{f(0) = 6(5)^0}}}
{{{f(0) = 6(1)}}}
{{{f(0) = 6}}}
So we get the proper output for the input x = 0. Repeat for the input x = 3 as well
{{{f(x) = 6(5)^x}}}
{{{f(3) = 6(5)^3}}}
{{{f(3) = 6(125)}}}
{{{f(3) = 750}}}
that output is correct as well. The function is confirmed. Both points are on the graph of this function curve.
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