Question

from unit 2, lesson 7
the output from a coal power plant is shown in the table:
energy in megawatts | number of days
1,200 | 2.4
1,800 | 3.6
4,000 | 8
10,000 | 20
similarly, the output from a solar power plant is shown in the table:
energy in megawatts | number of days
100 | 1
650 | 4
1,200 | 7
1,750 | 10
based on the tables, is the energy output in proportion to the number of days for either plant? if so, write an equation showing the relationship. if not, explain your reasoning.

Explanation:

Step1: Check coal plant proportionality

Calculate ratio of energy to days for each row:
$\frac{1200}{2.4}=500$, $\frac{1800}{3.6}=500$, $\frac{4000}{8}=500$, $\frac{10000}{20}=500$

Step2: Define coal plant relationship

Since ratios are equal, energy $E$ is proportional to days $d$. Let $E=kd$, substitute $k=500$:
$E=500d$

Step3: Check solar plant proportionality

Calculate ratio of energy to days for each row:
$\frac{100}{1}=100$, $\frac{600}{4}=150$, $\frac{1200}{7}\approx171.43$, $\frac{1750}{10}=175$

Step4: Analyze solar plant results

Ratios are not equal, so no proportional relationship.

Answer:

For the coal power plant: The energy output is proportional to the number of days. The equation is $E=500d$, where $E$ is energy in megawatts and $d$ is the number of days.
For the solar power plant: The energy output is not proportional to the number of days, because the ratio of energy output to number of days is not constant across all data pairs.