Comparing exponential and linear functions

Question

Find a formula for the exponential function.

 

(10,90) (30,10)

 

Round the value for to the nearest integer, and the value for to three decimal places.

 

y=ab^x, where

a =

and

b= 

Answer 1

substitute the x and y values into the  general exponential equation to get two new equations involving a & b.

 

90 = ab¹⁰

10 = ab³⁰

 

divide, giving 9 = b^-20  or 9b²⁰ = 1 so b = (1/9)

from which you get the lovely answer b = (1/9)^0.05  i.e. twentieth root of 0.1111111111111111111, approximately.

 

I'll let you compute that and also the value of a.