Question

The exponential function f, represented in the table, can be written as

f (x)=a*b^x

x | y
___
0| 9
1 | 15

complete the equation for F (x)

Answer 1

i put in 9 . (5/3)^x

Explanation:

and its wrong on kahn academy

the kahn academy answer is 15 . (3/5)^x

Answer 2

`$ f(x) = 9 \bigg((5)/(3) \bigg)^x $`

Explanation:

Note the f(0) = 9

and f(1) = 15

Since, f(x) = abˣ substituting for x, we get:

9 = f(0) = a . b⁰ = a

⇒ a = 9

Now, f(1) = 15

⇒ 15 = a . b¹

⇒ 15 = 9 . b

⇒ b =
`$ (15)/(9) $`

Therefore,
`$ f(x) = 9 . \bigg( (5)/(3) \bigg) ^x $`

Hence, the answer.