Question

According to a city's power authority, all streetlamps in the city can draw a percentage of power from a company's new solar panels. E(n) is a function that represents the relationship between the number of solar panels installed and the amount of energy generated per day in megawatt hours (MWh), where E(n) = 0.4n. D(e) is a function that represents the relationship between the number of days and the energy in (MWh) consumed by the street lamps in the city, where D(e) = 2e. Which of the following functions could be used to determine the number of days the streetlamps stay on, based on the number of solar panels installed? A) D(E(n)) = 2(0.4n) B) D(E(n)) = 2.4n C) E(D(e)) = (0.4n)(2e) D) E(D(e)) = 0.4(2e)

Answer 1

The correct function to determine the number of days streetlamps can stay on based on the number of solar panels installed is D(E(n)) = 2(0.4n), which represents the composition of the energy generation function E(n) with the energy consumption function D(e).

Step-by-step explanation:

The question involves finding a function that determines the number of days streetlamps can stay on based on the number of solar panels installed. Since E(n) represents the energy generated by n solar panels, and D(e) represents the energy consumption by street lamps over e days, we need to compose these functions to get the relationship between the number of panels and the number of days. Therefore, the correct function is the composition of D and E, D(E(n)), which is D(E(n)) = 2(0.4n). This expression essentially means that for each solar panel installed, 0.4 MWh of energy is generated, and the streetlamps consume 2 MWh of energy per day.