Question

The number of bacteria in a lab experiment can be modeled by the function

P
(
t
)
=
43
(
3
)
2
t
+
3
.
P(t)=43(3)
2t+3
. Write an equivalent function of the form
P
(
t
)
=
a
b
t
.
P(t)=ab
t

Answer 1

`P(t) = 1161(9)^(t)`

Explanation:

Given

`P(t) = 43(3)^(2t+3)`

Required

Write in form of
`P(t) =ab^t`

`P(t) = 43(3)^(2t+3)`

Apply law of indices:

`P(t) = 43(3)^(2t)*3^3}`

Reorder

`P(t) = 43*3^3*(3)^(2t)`

Express
`3^3` at 27

`P(t) = 43*27*(3)^(2t)`

`P(t) = 1161*(3)^(2t)`

Rewrite as:

`P(t) = 1161*(3^2)^(t)`

Express
`3^2` as 9

`P(t) = 1161*(9)^(t)`

`P(t) = 1161(9)^(t)`