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

Answer:

$P(t) = 1161(9)^{t}$

Step-by-step 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

$P(t) = 1161*(9)^{t}$

$P(t) = 1161(9)^{t}$