Question

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Answer 1

The relationship between the cost and the time of travel is a proportional

relation, such that as the time increases, the cost also increase.

The correct responses are as follows;

• 1. $\begin{tabular}{c|c|c|c|c}Years (t)&200&400&500\\Cost (c) &1,000&2,000&2,500\end{array}\right]$

• Please find attached the graph of the cost to travel forward in time

• 2. c = 5·t

• 3. $\begin{tabular}{c|c|c|c|c}Years (t)&200&400&500\\Cost (c) &1,000&2,000&2,500\end{array}\right]$

• The graph of the cost to go backward in time is attached

• 4. c = -15·t

• 5. The sign of the constant of proportionality are different because the direction of travel are different.

Reasons:

1. The amount charged per year for time travel = $5

The cost for 200 years travel = 200 × $5 = $1,000

The cost for 400 years travel = 400 × $5 = $2,000

Cost of 500 years travel = 500 × $5 = $2,500

The completed table is presented as follows;

$\begin{tabular}{c|c|c|c|c}Years (t)&200&400&500\\Cost (c) &1,000&2,000&2,500\end{array}\right]$

Please find attached the graph of the above data created with MS Excel

2. The equation for the graph is the equation that gives the cost, which is presented as follows;

Cost (c) = Years (t) × $5

• Which gives the equation; c = 5·t

3. The amount charged to go backward in time = $15 per year

Therefore, we have;

Cost for -200 years = 200 × $15 = $3,000

Cost to go back 400 years = 400 × $15 = $6,000

Cost to go back 500 years = 500 × $15 = $7,500

The completed table is presented as follows;

$\begin{tabular}{c|c|c|c|}Years (t)&-200&-400&-500\\Cost (c) &3,000&6,000& 7,500\end{array}\right]$

As the value of the time in years increases, the cost increases, therefore, the graph has a negative slope, which give;

The magnitude of the slope is the cost per year = $15

The equation for the graph is therefore; c = -15·t

5. The constant of proportionality are;

For c = 5·t; The constant of proportionality is 5

For c = -15·t; The constant of proportionality is -15

One constant is positive while the other is negative because, one goes forward in time while the other goes backward in time.

Learn more about proportional relations here:

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