Question

Write an exponential function in the form y=ab^x that goes through points (0,14) and (3,3024).

Answer 1

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

Explanation:

For an exponential function of the form y = a
`b^(x)`

Use the given points to find a and b

Using (0, 14 ), then

14 = a
`b^(0)` (
`b^(0)` = 1 ) , thus

a = 14

y = 14
`b^(x)`

Using (3, 3024 ) , then

3024 = 14 b³ ( divide both sides by 14 )

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

b =
`\sqrt[3]{216}` = 6 , thus

y = 14 ×
`6^(x)` ← exponential function