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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

The number of bacteria in a lab experiment can be modeled by the function P t 43 3 2 t 3 Pt433 2t3 Write an equivalent function of the form P t a b t Ptab t class=

Respuesta :

MrRoyal

Answer:

[tex]P(t) = 1161(9)^{t}[/tex]

Step-by-step explanation:

Given

[tex]P(t) = 43(3)^{2t+3}[/tex]

Required

Write in form of [tex]P(t) =ab^t[/tex]

[tex]P(t) = 43(3)^{2t+3}[/tex]

Apply law of indices:

[tex]P(t) = 43(3)^{2t}*3^3}[/tex]

Reorder

[tex]P(t) = 43*3^3*(3)^{2t}[/tex]

Express [tex]3^3[/tex] at 27

[tex]P(t) = 43*27*(3)^{2t}[/tex]

[tex]P(t) = 1161*(3)^{2t}[/tex]

Rewrite as:

[tex]P(t) = 1161*(3^2)^{t}[/tex]

Express [tex]3^2[/tex] as 9

[tex]P(t) = 1161*(9)^{t}[/tex]

[tex]P(t) = 1161(9)^{t}[/tex]

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