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1. It is common for electricity companies to charge varying amounts for electricity usage for different times throughout the day. Our local Mississauga Time Of

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1. It is common for electricity companies to charge varying amounts for electricity usage for different times throughout the day. Our local Mississauga Time Of Use rates can be seen in the table below. Current TOU Rates Midnight May 01, 2022 - Oct 31, 2022 Current Rate: Mid-Peak $0.1 13 per kWh 7:00AM to 1 1:00AM 5:00PM to 7:00PM 9:26 AM Ill $0.082 per kwh - Off-Peak Mid-Peak $0.113 per KWh - Mid-Peak $0.170 per KWh - On-Peak 11 10 Noon Figure 1: Time of use rates for Alectra Utilities. Source: https: //alectrautilities. com/time-use-pricing Note: 1 KW = 1000 W. The amount of energy (measured in kilowatt-hours) is given by multiplying power measured in KW), by time (measured in hours). (a) (1 mark) A typical outdoor porch light is rated at 40 Watts (W). How many kilowatt-hours (KWh) does a 40W porch light use in one day? (In 24 hours.) (b) (2 marks) How much would it cost to leave the porch light on for the entire month of September using the rates listed in Figure 1? (c) (2 marks) If your bill indicated you spent $10 on off-peak electricity (and nothing else), could you calculate how much energy (in KWh) you used? Does your ability to calculate your total energy usage change if your bill only listed a total dollar amount for all three usages rates? (d) (3 marks) Electricity rates in Ontario have decreased since the start of the pandemic (unlike in many other jurisdictions). On January 1, 2020, the off-peak rate was 12.8 cents/kWh and on May 1, 2022 the same tier is 8.2 cents/KWh. If we assume a continuous compounding model, the off-peak rate R(t) as a function of t months since January 1, 2020 is given by R(t) - Roett where Ro is the rate on January 1, 2020. Find an exact formula for R(t) - Roe" by determining the values for Ro and r. Answer in exact form (do not round any values). (e) (2 marks) Use your answer in (d) to compute the predicted off-peak electricity rate on January 1, 2025 and on January 1, 2035. Use a calculator to round your final answers to 2 decimal places. Based on your answers, comment briefly on whether this mathematical model for the cost of electricity seems suitable for long-term predictions. Important: 4 marks are also given based on the quality of your writing and your explanations

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