Exercise 46 Page 205

Practice makes perfect

a Let's list the ordered pairs from the graph.

We can use these values to find the common difference of this arithmetic sequence.

The sequence has a common difference of - 8. In the list we can also see that the first term is 56. Let's substitute these values into the function for an arithmetic sequence.

f(n)=a_1+(n-1)d

SubstituteII

a_1= 56, d= -8

f(n)= 56+(n-1)( -8)

Distr

Distribute -8

f(n)=56-8n+8

AddTerms

Add terms

f(n)=64-8n

The function f(n)=64-8n represents the arithmetic sequence.

b We will use the function from Part A to find the value of n when f(n)=16.

f(n)=64-8n

Substitute

f(n)= 16

16=64-8n

▼

Solve for n

SubEqn

LHS-64=RHS-64

-48=-8n

DivEqn

.LHS /(-8).=.RHS /(-8).

6=n

RearrangeEqn

Rearrange equation

n=6

The movie earns $16 million in week 6.

c We know that the common difference is - 8. We can use this to continue the arithmetic sequence from the last recorded ordered pair until we reach the week when the earnings are 0.

... 32 -8 → 24 -8 → 16 -8 → 8-8 → 0This gives us the following arithmetic sequence. 56, 48, 40, 32, 24, 16, 8, 0 Let's add all of these using a calculator.

Calculator window showing the addition of the terms

The sum is 224, which means the movie earns a total of $224 million.

Subchapter links

Communicate Your Answer p.199

Monitoring Progress p.200-203

Exercises p.204-206

Exercise 46 Page 205

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