Chapter 4.6, Problem 45E

(a)

To determine

To write: a function that represents arithmetic sequence.

Answer to Problem 45E

the function that represents the arithmetic sequence is $f(n)=5n$

Explanation of Solution

Given:

Minutes after midnight January 1st	1	2	3	4
Total babies born	5	10	15	20

Calculation:

The first term is 5 and the common difference is 5

Consider the function for the arithmetic sequence

  $f(n)=a_1+(n-1)d$

Put the value $a_1=5$ and $d=5$

  $\begin{array}{l}f(n)=5+(n-1)(5)\\ =5+5n-5\\ =5n\end{array}$

Therefore, the function that represents the arithmetic sequence is $f(n)=5n$

Conclusion:

Therefore, the function that represents the arithmetic sequence is $f(n)=5n$

(b)

To determine

To graph: the function.

Answer to Problem 45E

The graph for the sequence

  

Explanation of Solution

Calculation:

Now, draw the graph for the sequence

  

Conclusion:

Therefore, the graph for the sequence is drawn.

(c)

To determine

To estimate: the minutes after midnight January 1st it takes for 100 babies to be born

Answer to Problem 45E

The minutes after midnight January 1st it takes for 100 babies to be born is 20 minutes

Explanation of Solution

Calculation:

Now find the value of $n$ for which $f(n)=100$

So,

  $f(n)=1005n=100$

Divide by 5 on both sides

  $n=20$

Therefore, the minutes after midnight January 1st it takes for 100 babies to be born is 20 minutes

Conclusion:

Therefore, the minutes after midnight January 1st it takes for 100 babies to be born is 20 minutes