Chapter 4.6, Problem 46E

a.

To determine

To write: A function that represents the arithmetic sequence.

Answer to Problem 46E

Function that represents the arithmetic sequence is $64-8n$ .

Explanation of Solution

Given information: From graph we get sequence is $56,48,40,32$ .

Calculation: Given sequence is $56,48,40,32$ .

Common difference is $a_2-a_1=48-56=-8$ .

  $nth$ Term of arithmetic sequence is $a_n=a+(n-1)d$ .

Put $a=56\mathrm{and}d=-8$

  $\begin{array}{l}{s}_n=\frac{n}{2}(a+l)\\ s_4=\frac{4}{2}(54+32)\\ s_4=2(86)\\ s_4=172\end{array}$

Therefore function that represents the arithmetic sequence is $64-8n$ .

b.

To determine

To find: In what week does the movie earn $\$16$ million?

Answer to Problem 46E

In $6th$ week movie earn $\$16$ million.

Explanation of Solution

Given information: From first part $a_n=64-8n$ .

Calculation: $a_n=64-8n$ .

  $a_n=16$

Compare both equation we get

  $\begin{array}{l}64-8n=16\\ 64-16=8n\\ 48=8n\\ \frac{48}{8}=n\\ 6=n\end{array}$

Therefore In $6th$ week movie earn $\$16$ million.

c.

To determine

To find: How much money does the movie earn overall.

Answer to Problem 46E

Movie earn overall is

  $\$172$ million.

Explanation of Solution

Given information: From graph we get sequence is $56,48,40,32$ .

Calculation: Given sequence is $56,48,40,32$ .

  $\begin{array}{l}{s}_n=\frac{n}{2}(a+l)\\ s_4=\frac{4}{2}(54+32)\\ s_4=2(86)\\ s_4=172\end{array}$

Therefore movie earn overall is $\$172$ million.