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.

List of the ordered pairs with common difference marked.

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 in 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

In week 6 the movie earns $16 million.

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 → 0

This 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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