Surds and indices

Question

The curve y=axⁿ-23 passes through (3,4), (9,220) and (-1,k). Find the values of a, n and k.

 

Ans: a=3, n=2 and k=-20

 

Thank You!:)

Answer 1

Using the first two points we get the equations

 

27 =  a  3ⁿ    and   243 = a  9ⁿ

 

Dividing the second one of these by the first gives

 

  243/ 27 = 9 =  9ⁿ / 3ⁿ    =  3²ⁿ / 3ⁿ   =  3ⁿ  

 

since 9 is equal to 3²     we conclude that  n = 2

 

With this, from the first equation       27 =   a 3²  =  9 a       and a = 3

 

The last point gives the equation   k =  3 (-1)²   - 23     so k = - 20