Question

Question 2 An exponential model y = a.6 passes through the points (0,9) and (3,243). What are the values of a and b?​

Answer 1

a = 9, b = 3

Explanation:

The exponential function is

y = a
`b^(x)`

Find a and b by using the points it passes through

Using (0, 9 ) then

9 = a
`b^(0)` (
`b^(0)` = 1 )

a = 9

y = 9
`b^(x)`

Using (3, 243 ) then

243 = 9b³ ( divide both sides by 9 )

27 = b³ ( take the cube root of both sides )

b =
`\sqrt[3]{27}` = 3

y = 9
`(3)^(x)` ← exponential equation