Question

Write an exponential function in the form y=ab^x that goes through the points (0,14) and (6,896)

Answer 1

y = 14
`(2)^(x)`

Explanation:

Find a and b by substituting the points into the equation

using (0, 14 ) , then

14 = a
`b^(0)` [
`b^(0)` = 1 ] , then

14 = a × 1 ⇒ a = 14

y = 14
`b^(x)`

using (6, 896 )

896 = 14
`b^(6)` ( divide both sides by 14 )

64 =
`b^(6)` ( take the sixth root of both sides )

b =
`\sqrt[6]{64}` = 2

Then

y = 14
`(2)^(x)` ← is the exponential function