Answer: Q(t) = 410*(5)^(2t) = 410*(5^2)^t = 410*(25)^t
Step-by-step explanation:
We start with the equation:
Q(t) = 410*(5)^(2t)
And we want to rewrite this in the form:
Q(t) = a*b^t
To do this, we need to use the property:
(a^x)^y = a^(x*y)
Using this, we can rewrite:
Q(t) = 410*(5)^(2t) = 410*(5^2)^t = 410*(25)^t
And this is the form that we wanted:
Answer:
13120(16)^t
Step-by-step explanation:
The number of views on a viral video can be modeled by the function Q(t)=820(4)^{2t+2}.Q(t)=820(4)
2t+2
. Write an equivalent function of the form Q(t)=ab^t.Q(t)=ab
t
.
Q(t)=
Q(t)=
\,\,820(4)^{2t+2}
820(4)
2t+2
Q(t)=
Q(t)=
\,\,820\cdot\color{steelblue}{4^{2t+2}}
820⋅4
2t+2
Q(t)=
Q(t)=
\,\,820\cdot\color{steelblue}{4^{2t}\cdot 4^{2}}
820⋅4
2t
⋅4
2
\small 4^a\cdot4^b \rightarrow 4^{a+b},4
a
⋅4
b
→4
a+b
, but going backwards \small 4^{a+b}\rightarrow 4^a\cdot 4^b4
a+b
→4
a
⋅4
b
Q(t)=
Q(t)=
\,\,820\cdot\color{steelblue}{4^{2}\cdot 4^{2t}}
820⋅4
2
⋅4
2t
Switch order of multiplication
Q(t)=
Q(t)=
\,\,(820\cdot\color{steelblue}{16})\cdot \color{steelblue}{4^{2t}}
(820⋅16)⋅4
2t
Evaluate \color{steelblue}{4^{2}=16}4
2
=16
Q(t)=
Q(t)=
\,\,13120(4)^{2t}
13120(4)
2t
Multiply 820\cdot 16=820⋅16=1312013120
Q(t)=
Q(t)=
\,\,13120(4^{2})^{t}
13120(4
2
)
t
Since (4^a)^b\rightarrow 4^{ab},(4
a
)
b
→4
ab
, we can go backwards 4^{ab}\rightarrow (4^a)^b4
ab
→(4
a
)
b
Q(t)=
Q(t)=
\,\,13120(16)^{t}
13120(16)
t
Evaluate 4^{2}=164
2
=16
