Question

Write an exponential function in the form

y
=
a
b
x
y=ab
x
that goes through points
(
0
,
4
)
(0,4) and
(
3
,
2916
)
(3,2916).

Answer 1

y = 4
`(9)^(x)`

Explanation:

Using the given points to find a and b

Using (0, 4), then

4 = a
`b^(0)` ⇒ a = 4, thus

y = 4
`b^(x)`

Using (3, 2916), then

2916 = 4 b³ ( divide both sides by 4 )

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

b =
`\sqrt[3]{729}` = 9

Thus

y = 4
`9^(x)` ← is the exponential function