Write an exponential function y=ab^x for a graph that includes (-2,2/25) and (1,10).

Expert Answers
lemjay eNotes educator| Certified Educator

To determine the exponential function, plug-in the point (-2,2/25) to y=ab^x.


Then, simplify the equation.



And, isolate a.


`2/25b^2=a `        (Let this be EQ1.)

Next, plug-in the second point (1,10) to y=ab^x.



From here, plug-in EQ1.



Then, isolate b.





And, plug-in the value of to EQ1 to solve for value of a.


Then, plug-in the value of a and b to y=ab^x.

Hence, the exponential function is `y=2*5^x` .

oldnick | Student


`ab^-2=2/25`   (1)

  `ab=10`     (2)

we have set condirions   y=ab^x  for the points  `(-2:2/25)`  and

`(1;10)`  so its a system a two varibales:

dividing (2) by (1) we get:


`(ab) : (ab^-2)=(ab)(a^-1b^2)=b^3= ` `10:(2/25)=(10)(25)/2=`

`=125`        `b=5` from (2) we have `a=2`   so:




The fnction as in the graph is.

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