Question

the table shows the number of views, in millions per day, of a music video that is viewed on two different websites. if the pattern for each website continues, which website will have more views after one month and why? time (days) website a (in millions) website b (in millions) 0 0 1 1 1 3 2 10 9 3 29 27 views of a music video website a, because the number of views is growing at a cubic rate. website b, because the number of views is growing exponentially. website a, because the number of views is growing exponentially. website a and b will have the same number of views, because they will both reach a maximum number of viewers.

Explanation:

Step1: Analyze growth pattern of Website A

Let's assume the relationship for Website A is of the form $y = ax^{3}+bx^{2}+cx + d$. Using the points $(0,0)$: $0=a(0)^{3}+b(0)^{2}+c(0)+d$, so $d = 0$. Using $(1,1)$: $1=a(1)^{3}+b(1)^{2}+c(1)$, i.e., $a + b + c=1$. Using $(2,10)$: $10=a(2)^{3}+b(2)^{2}+c(2)=8a + 4b+2c$. Using $(3,29)$: $29=a(3)^{3}+b(3)^{2}+c(3)=27a+9b + 3c$. Solving the system of equations

$$\begin{cases}a + b + c=1\\8a + 4b+2c=10\\27a+9b + 3c=29\end{cases}$$

, we find the growth is cubic.

Step2: Analyze growth pattern of Website B

The values for Website B are $1,3,9,27$. We can see that the general - term formula is $y = 3^{x}$, which is an exponential growth function of the form $y = a\cdot r^{x}$ where $a = 1$ and $r=3$.

Step3: Compare long - term growth

In the long - term, exponential functions ($y = a\cdot r^{x},r>1$) grow faster than polynomial functions. As time (number of days) increases, the exponential growth of Website B will outpace the cubic growth of Website A.

Answer:

B. Website B, because the number of views is growing exponentially.