Question

a space program is testing a series of new rockets to decide which one to use for the upcoming mars mission. the table shows information about the power consumption (p) in kw of electricity in terms of time (t) in hours.
rocket a: power consumption is modeled by the equation p = 1.4t.
rocket b: power consumption is modeled in the table.
which rocket would use less power if the trip takes only 5 hours? explain your reasoning. enter the answer.

Explanation:

Step1: Find power consumption of Rocket A

Given the equation \(p = 1.4t\) for Rocket A. When \(t = 5\) hours, substitute \(t\) into the equation.
\(p_{A}=1.4\times5\)
\(p_{A}=7\) kW

Step2: Find power consumption of Rocket B

From the table of Rocket B, assume the relationship is linear. The ratio of \(p\) to \(t\) is \(\frac{3}{2}=\frac{6}{4}=\frac{9}{6}=\frac{12}{8}=\frac{15}{10}=1.5\). So the equation for Rocket B is \(p = 1.5t\). When \(t = 5\) hours, substitute \(t\) into the equation.
\(p_{B}=1.5\times5\)
\(p_{B}=7.5\) kW

Step3: Compare power consumptions

Compare \(p_{A}\) and \(p_{B}\). Since \(7<7.5\)

Answer:

Rocket A would use less power. Because when \(t = 5\), \(p_{A}=1.4\times5 = 7\) kW and \(p_{B}=1.5\times5=7.5\) kW, and \(7<7.5\)