Exercise 45 Page 205

Practice makes perfect

a To write a function representing an arithmetic sequence with the first term a_1 and common difference d, we can use the following equation.

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

From the table we can see that the first term is 5. We can also see that the difference between each pair of consecutive terms (the common difference) is 5. Let's substitute these values into the equation.

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

SubstituteII

a_1= 5, d= 5

f(n)= 5+(n-1) 5

Distr

Distribute 5

f(n)=5+5n-5

SubTerm

Subtract term

f(n)=5n

The function f(n)=5n represents the arithmetic sequence.

b From the table let's identify the ordered pairs (n,a_n) we need to graph.

Minutes after January 1st	1	2	3	4
Total babies born	5	10	15	20
Ordered pairs	(1,5)	(2,10)	(3,15)	(4,20)

Let's plot them on a coordinate plane.

c We will use the function from Part A to find the value of n when f(n)=100.

f(n)=5n

Substitute

f(n)= 100

100=5n

DivEqn

.LHS /5.=.RHS /5.

20=n

RearrangeEqn

Rearrange equation

n=20

From midnight on January 1st it takes 20 minutes for 100 babies to be born.

Subchapter links

Communicate Your Answer p.199

Monitoring Progress p.200-203

Exercises p.204-206

Exercise 45 Page 205

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