How do you find the equation of an exponential function with only two points, (2,90) and (3,270)?

Question

The two points given are (2,90) and (3,270)

Answer 1

The general form for an exponential equation is f(x) = a*b^x. To find the equation, you need to find the values of a and b.

 

    1.  To find b, take the ratio of f at the two known points, f(3)/f(2)):

 

  270/90 = a*b³/a*b² = b
  3 = b

 

    2.  So far we have f(x) = a*3^x.  To find the value of a, plug in one of the known points.  I'll use (2,90):

 

 f(2) = a*3²

 90 = a*9

 90/9 = a

 10 = a

 

The full equation is f(x) = 10*3^x

 

Answer 2

f(x) = ab^x

90 = ab²

270 = ab³

ab³ / ab² = b

270 / 90 = 3

b = 3

f(x) = a(3)^x

90 = a(9)

10 = a

f(x) = 10(3)^x