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 be 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 Dina how much electricity was used per person between 2000 and 2008 ?Choose 1 answer:(A) E(t)=12,300⋅(1.06)t(B) E(t)=12,300⋅(0.06)t(C) E(t)=12,300+(1.06)⋅t(D) E(t)=12,300+(0.06)⋅t
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 be 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 Dina how much electricity was used per person between 2000 and 2008 ?Choose 1 answer:(A) E(t)=12,300⋅(1.06)t(B) E(t)=12,300⋅(0.06)t(C) E(t)=12,300+(1.06)⋅t(D) E(t)=12,300+(0.06)⋅t
Identify Growth Rate: We need to find a formula that shows a 6% growth each year. Since it's a percentage growth, we're dealing with exponential growth, not linear.
Base Formula for Exponential Growth: The base formula for exponential growth is Initial Value ×(1+Growth Rate)t, where t is the number of years after the initial year.
Plug in Values: Plug in the values: Initial Value is 12,300 kilowatt-hours, Growth Rate is 6% or 0.06, and t is the number of years after 2000.
Final Formula: The correct formula should be E(t)=12,300×(1+0.06)t, which simplifies to E(t)=12,300×(1.06)t.
Compare Options: Comparing the options, we see that option (A) matches our formula: E(t)=12,300×(1.06)t.
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