Chapter 4.6, Problem 45E

a.

To determine

To write: A function that represent the arithmetic sequence.

Answer to Problem 45E

Required function that represents the arithmetic sequence is $a_n=5n$

Explanation of Solution

Given information: Given sequence is $5,10,15,20,\mathrm{.....}$ .

Calculation: Given sequence is $5,10,15,20,\mathrm{.....}$ .

Common difference $=a_2-a_1=10-5=5$ .

  $n\mathrm{th}$ Term of arithmetic sequence is $a_n=a+(n-1)d$

Here $a=5\mathrm{and}d=5$ put this value in $a_n$

  $\begin{array}{l}{a}_n=a+(n-1)d\\ a_n=5+(n-1)5\\ a_n=5+5n-5\\ a_n=5n\end{array}$

Therefore required function that represents the arithmetic sequence is $a_n=5n$ .

ii.

To determine

To draw: The function.

Answer to Problem 45E

Graph of this function is:

  

Explanation of Solution

Given information: Given sequence is $5,10,15,20,\mathrm{.....}$ .

Calculation: Given sequence is $5,10,15,20,\mathrm{.....}$ .

Graph of this sequence is:

  

c.

To determine

To estimate: How many minutes after midnight January $1st$ it takes for $100$ babies to be born.

Answer to Problem 45E

  $20$ Minutes after midnight January $1st$ it takes for $100$ babies born.

Explanation of Solution

Given information: Given sequence is $5,10,15,20,\mathrm{.....}$ .

In first part we find $n\mathrm{th}$ term of the sequence is $a_n=5n$ .

Calculation: Given sequence is $5,10,15,20,\mathrm{.....}$ .

In first part we find $n\mathrm{th}$ term of the sequence is $a_n=5n$ .

Total number of babies born is $100$ .

  $\begin{array}{l}{a}_n=100\\ 5n=100\\ n=\frac{100}{5}=20\end{array}$

Therefore $20$ minutes after midnight January $1st$ it takes for $100$ babies born.