Answer :
Below is a detailed step‐by‐step solution.
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Step 3: Odometer Reading Problem
A car’s odometer initially reads
[tex]$$15,\!000 \text{ miles.}$$[/tex]
During the trip, the car travels at a constant speed of
[tex]$$65 \text{ miles per hour.}$$[/tex]
a) To complete the table, we add the distance traveled each hour to the previous reading.
• At time 0 hours, the reading is:
[tex]$$15,\!000.$$[/tex]
• After 1 hour, the car travels 65 miles, so the reading is:
[tex]$$15,\!000 + 65 = 15,\!065.$$[/tex]
• After 2 hours, another 65 miles are added:
[tex]$$15,\!065 + 65 = 15,\!130.$$[/tex]
• After 3 hours, we get:
[tex]$$15,\!130 + 65 = 15,\!195.$$[/tex]
• After 4 hours, the reading becomes:
[tex]$$15,\!195 + 65 = 15,\!260.$$[/tex]
Thus, the completed table is:
[tex]$$
\begin{array}{|c|c|}
\hline
\text{Duration of Trip (hours)} & \text{Odometer Reading (miles)} \\
\hline
0 & 15,\!000 \\
\hline
1 & 15,\!065 \\
\hline
2 & 15,\!130 \\
\hline
3 & 15,\!195 \\
\hline
4 & 15,\!260 \\
\hline
\end{array}
$$[/tex]
b) Notice that the difference between any hour’s reading and that of the previous hour is always
[tex]$$65 \text{ miles.}$$[/tex]
This constant difference confirms that the car travels the same distance every hour.
c) If the odometer reads [tex]$n$[/tex] miles at a particular hour, then one hour later the reading will be:
[tex]$$n + 65.$$[/tex]
──────────────────────────────
Step 4: Doubling the Number of People Who Read a Book
Initially, at the beginning of January (month 0), the number of people who have read the book is
[tex]$$300.$$[/tex]
The number doubles each month. This means that the number of people after each month is given by the formula:
[tex]$$\text{Number at month } m = 300 \cdot 2^m.$$[/tex]
So, we calculate:
• For month 0:
[tex]$$300 \cdot 2^0 = 300 \cdot 1 = 300.$$[/tex]
• For month 1:
[tex]$$300 \cdot 2^1 = 300 \cdot 2 = 600.$$[/tex]
• For month 2:
[tex]$$300 \cdot 2^2 = 300 \cdot 4 = 1,\!200.$$[/tex]
• For month 3:
[tex]$$300 \cdot 2^3 = 300 \cdot 8 = 2,\!400.$$[/tex]
The completed table is:
[tex]$$
\begin{array}{|c|c|}
\hline
\text{Number of Months Since January} & \text{Number of People Who Have Read the Book} \\
\hline
0 & 300 \\
\hline
1 & 600 \\
\hline
2 & 1,\!200 \\
\hline
3 & 2,\!400 \\
\hline
\end{array}
$$[/tex]
──────────────────────────────
Final Answers:
1. Odometer Table:
[tex]$$
\begin{array}{|c|c|}
\hline
\text{Duration of Trip (hours)} & \text{Odometer Reading (miles)} \\
\hline
0 & 15,\!000 \\
\hline
1 & 15,\!065 \\
\hline
2 & 15,\!130 \\
\hline
3 & 15,\!195 \\
\hline
4 & 15,\!260 \\
\hline
\end{array}
$$[/tex]
2. The difference between the odometer reading any hour and the previous hour is always
[tex]$$65 \text{ miles.}$$[/tex]
3. If the odometer reads [tex]$n$[/tex] miles at a particular hour, one hour later it will read
[tex]$$n + 65.$$[/tex]
4. Doubling Table for the Number of People:
[tex]$$
\begin{array}{|c|c|}
\hline
\text{Number of Months Since January} & \text{Number of People Who Have Read the Book} \\
\hline
0 & 300 \\
\hline
1 & 600 \\
\hline
2 & 1,\!200 \\
\hline
3 & 2,\!400 \\
\hline
\end{array}
$$[/tex]
This completes our detailed solution.
──────────────────────────────
Step 3: Odometer Reading Problem
A car’s odometer initially reads
[tex]$$15,\!000 \text{ miles.}$$[/tex]
During the trip, the car travels at a constant speed of
[tex]$$65 \text{ miles per hour.}$$[/tex]
a) To complete the table, we add the distance traveled each hour to the previous reading.
• At time 0 hours, the reading is:
[tex]$$15,\!000.$$[/tex]
• After 1 hour, the car travels 65 miles, so the reading is:
[tex]$$15,\!000 + 65 = 15,\!065.$$[/tex]
• After 2 hours, another 65 miles are added:
[tex]$$15,\!065 + 65 = 15,\!130.$$[/tex]
• After 3 hours, we get:
[tex]$$15,\!130 + 65 = 15,\!195.$$[/tex]
• After 4 hours, the reading becomes:
[tex]$$15,\!195 + 65 = 15,\!260.$$[/tex]
Thus, the completed table is:
[tex]$$
\begin{array}{|c|c|}
\hline
\text{Duration of Trip (hours)} & \text{Odometer Reading (miles)} \\
\hline
0 & 15,\!000 \\
\hline
1 & 15,\!065 \\
\hline
2 & 15,\!130 \\
\hline
3 & 15,\!195 \\
\hline
4 & 15,\!260 \\
\hline
\end{array}
$$[/tex]
b) Notice that the difference between any hour’s reading and that of the previous hour is always
[tex]$$65 \text{ miles.}$$[/tex]
This constant difference confirms that the car travels the same distance every hour.
c) If the odometer reads [tex]$n$[/tex] miles at a particular hour, then one hour later the reading will be:
[tex]$$n + 65.$$[/tex]
──────────────────────────────
Step 4: Doubling the Number of People Who Read a Book
Initially, at the beginning of January (month 0), the number of people who have read the book is
[tex]$$300.$$[/tex]
The number doubles each month. This means that the number of people after each month is given by the formula:
[tex]$$\text{Number at month } m = 300 \cdot 2^m.$$[/tex]
So, we calculate:
• For month 0:
[tex]$$300 \cdot 2^0 = 300 \cdot 1 = 300.$$[/tex]
• For month 1:
[tex]$$300 \cdot 2^1 = 300 \cdot 2 = 600.$$[/tex]
• For month 2:
[tex]$$300 \cdot 2^2 = 300 \cdot 4 = 1,\!200.$$[/tex]
• For month 3:
[tex]$$300 \cdot 2^3 = 300 \cdot 8 = 2,\!400.$$[/tex]
The completed table is:
[tex]$$
\begin{array}{|c|c|}
\hline
\text{Number of Months Since January} & \text{Number of People Who Have Read the Book} \\
\hline
0 & 300 \\
\hline
1 & 600 \\
\hline
2 & 1,\!200 \\
\hline
3 & 2,\!400 \\
\hline
\end{array}
$$[/tex]
──────────────────────────────
Final Answers:
1. Odometer Table:
[tex]$$
\begin{array}{|c|c|}
\hline
\text{Duration of Trip (hours)} & \text{Odometer Reading (miles)} \\
\hline
0 & 15,\!000 \\
\hline
1 & 15,\!065 \\
\hline
2 & 15,\!130 \\
\hline
3 & 15,\!195 \\
\hline
4 & 15,\!260 \\
\hline
\end{array}
$$[/tex]
2. The difference between the odometer reading any hour and the previous hour is always
[tex]$$65 \text{ miles.}$$[/tex]
3. If the odometer reads [tex]$n$[/tex] miles at a particular hour, one hour later it will read
[tex]$$n + 65.$$[/tex]
4. Doubling Table for the Number of People:
[tex]$$
\begin{array}{|c|c|}
\hline
\text{Number of Months Since January} & \text{Number of People Who Have Read the Book} \\
\hline
0 & 300 \\
\hline
1 & 600 \\
\hline
2 & 1,\!200 \\
\hline
3 & 2,\!400 \\
\hline
\end{array}
$$[/tex]
This completes our detailed solution.