Dina is conducting a study on the amount of electricity used per person in the country of Qatar. She finds that from the year 2000 to 2008, the amount of electricity used per person grew by an average of 6% from one year to the next. Let e(t) be the amount of electricity used per person in kilowatt-hours and t the number of years after 2000. If the amount of electricity used per person in 2000 was approximately 12,300 kilowatt-hours, which of the following mathematical models will give Dana how much electricity was used per person between 2000 and 2008?
Q. Dina is conducting a study on the amount of electricity used per person in the country of Qatar. She finds that from the year 2000 to 2008, the amount of electricity used per person grew by an average of 6% from one year to the next. Let e(t) be the amount of electricity used per person in kilowatt-hours and t the number of years after 2000. If the amount of electricity used per person in 2000 was approximately 12,300 kilowatt-hours, which of the following mathematical models will give Dana how much electricity was used per person between 2000 and 2008?
Identify Initial Data: Identify the initial amount of electricity used and the growth rate.Initial electricity usage in 2000: 12,300 kilowatt-hours.Annual growth rate: 6%.
Use Exponential Growth Formula: Use the formula for exponential growth to model the electricity usage.The formula for exponential growth is e(t)=e0×(1+r)t where:- e0 is the initial amount (12,300 kilowatt-hours),- r is the growth rate (0.06),- t is the number of years after 2000.
Calculate Electricity Usage in 2008: Calculate the amount of electricity used in 2008, which is 8 years after 2000.Plug in the values into the formula: e(8)=12,300×(1+0.06)8.
Perform Calculation: Perform the calculation.e(8)=12,300×1.068e(8)=12,300×1.59385 (using a calculator for 1.068)e(8)=19,604.345 kilowatt-hours.
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