Chapter 11.1, Problem 32PPS

(a)

To determine

Find the time he will row on the 18^th day.

Answer to Problem 32PPS

30.5 minutes

Explanation of Solution

Given:

Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day.

How long will he row on the 18^th day?

Concept Used:

He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day.

  $a_1=5\text{and}d=1\min 30\text{seconds}=1.5\text{minutes}\text{and}n=18$

Calculation:

The general equation for nth term: $a_n=a_1+(n-1)d$

  $a_1=5\text{and}d=1\min 30\text{seconds}=1.5\text{minutes}\text{and}n=18$

Now find the 18^th term of the sequence:

  $\begin{array}{l}{a}_n=a_1+(n-1)d\\ a_{18}=5+(18-1)·1.5\\ a_{18}=5+25.5\\ a_{18}=30.5\end{array}$

Thus, on 18^th day he will row 30.5 minutes.

(b)

To determine

Find the day when he will first row an hour or more.

Answer to Problem 32PPS

38^th day

Explanation of Solution

Given:

Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day.

On what day will first row an hour or more?

Concept Used:

He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day.

  $a_1=5\text{and}d=1\min 30\text{seconds}=1.5\text{minutes}\text{and}{a}_n=60$

Calculation:

The general equation for nth term: $a_n=a_1+(n-1)d$

  $a_1=5\text{and}d=1\min 30\text{seconds}=1.5\text{minutes}\text{and}{a}_n=60$

Find n:

  $\begin{array}{l}{a}_n=a_1+(n-1)d\\ 60=5+(n-1)·1.5\\ 60=5+1.5n-1.5\\ 60=3.5+1.5n\\ 60-3.5=3.5-3.5+1.5n\\ 56.5=1.5n\\ \frac{56.5}{1.5}=\frac{1.5n}{1.5}\\ n=37.666\end{array}$

On 38^th day Mario will first row an hour or more.

Thus, on 38^th day Mario will first row an hour or more.

(c)

To determine

Explain how this pattern continues indefinitely.

Answer to Problem 32PPS

The pattern will probably not continue indefinitely

Explanation of Solution

Given:

Mario began an exercise program to get back in shape. He plans to row 5 minutes on his rowing machine the first day and increase his rowing time by one minute and thirty seconds each day.

Is it reasonable for this pattern to continue indefinitely? Explain.

Concept Used:

The pattern will probably not continue indefinitely because as the number of days grows, it will assume he rows for an infinite amount of time. It is doubtful that he can row for hours on end.

Thus, the pattern will probably not continue indefinitely