Question

1. jada saw a music video that her favorite artist recently posted online. the equation ( v(t) = 320 cdot 4^t ) represents the number of views, ( v ), of the video, ( t ) days since jada saw the video. assume that the equation makes sense for a few days before and after jada saw the video.

a) find ( v(-2) ).
b) what does ( v(-2) ) represent in this situation?

1. for the equation ( y = 8 cdot 2^x ), complete the table and plot the ordered pairs on the graph.

(table with x values -3, -2, -1, 0, 1, 2, 3 and empty y column, followed by a graph)

Explanation:

Step1: Substitute $t=-2$ into $v(t)$

$v(-2)=320 \cdot 4^{-2}$

Step2: Rewrite negative exponent as reciprocal

$v(-2)=320 \cdot \frac{1}{4^2}$

Step3: Calculate $4^2$ and simplify

$v(-2)=320 \cdot \frac{1}{16}=20$

Step4: Substitute $x=-3$ into $y=8 \cdot 2^x$

$y=8 \cdot 2^{-3}=8 \cdot \frac{1}{8}=1$

Step5: Substitute $x=-2$ into $y=8 \cdot 2^x$

$y=8 \cdot 2^{-2}=8 \cdot \frac{1}{4}=2$

Step6: Substitute $x=-1$ into $y=8 \cdot 2^x$

$y=8 \cdot 2^{-1}=8 \cdot \frac{1}{2}=4$

Step7: Substitute $x=0$ into $y=8 \cdot 2^x$

$y=8 \cdot 2^{0}=8 \cdot 1=8$

Step8: Substitute $x=1$ into $y=8 \cdot 2^x$

$y=8 \cdot 2^{1}=8 \cdot 2=16$

Step9: Substitute $x=2$ into $y=8 \cdot 2^x$

$y=8 \cdot 2^{2}=8 \cdot 4=32$

Step10: Substitute $x=3$ into $y=8 \cdot 2^x$

$y=8 \cdot 2^{3}=8 \cdot 8=64$

Answer:

For 5a):

20

For 5b):

It represents the number of views the video had 2 days before Jada saw it.

For 6) Completed Table:

$x$	-3	-2	-1	0	1	2	3

For 6) Graph Plotting:

Plot the ordered pairs $(-3,1)$, $(-2,2)$, $(-1,4)$, $(0,8)$, $(1,16)$, $(2,32)$, $(3,64)$ on the provided coordinate grid, with each point aligned to the corresponding $x$ and $y$ axis values.