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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

Dina is conducting a study on the amount of electricity used per person in the country of Qatar. She finds that from the year 20002000 to 20082008 , the amount of electricity used per person grew by an average of 6% 6 \% from one year to the next.\newlineLet E(t) E(t) be the amount of electricity used per person in kilowatt-hours and t t be the number of years after 20002000 . If the amount of electricity used per person in 20002000 was approximately 1212,300300 kilowatt-hours, which of the following mathematical models will give Dina how much electricity was used per person between 20002000 and 20082008 ?\newlineChoose 11 answer:\newline(A) E(t)=12,300(1.06)t E(t)=12,300 \cdot(1.06)^{t} \newline(B) E(t)=12,300(0.06)t E(t)=12,300 \cdot(0.06)^{t} \newline(C) E(t)=12,300+(1.06)t E(t)=12,300+(1.06) \cdot t \newline(D) E(t)=12,300+(0.06)t E(t)=12,300+(0.06) \cdot t

Full solution

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 20002000 to 20082008 , the amount of electricity used per person grew by an average of 6% 6 \% from one year to the next.\newlineLet E(t) E(t) be the amount of electricity used per person in kilowatt-hours and t t be the number of years after 20002000 . If the amount of electricity used per person in 20002000 was approximately 1212,300300 kilowatt-hours, which of the following mathematical models will give Dina how much electricity was used per person between 20002000 and 20082008 ?\newlineChoose 11 answer:\newline(A) E(t)=12,300(1.06)t E(t)=12,300 \cdot(1.06)^{t} \newline(B) E(t)=12,300(0.06)t E(t)=12,300 \cdot(0.06)^{t} \newline(C) E(t)=12,300+(1.06)t E(t)=12,300+(1.06) \cdot t \newline(D) E(t)=12,300+(0.06)t E(t)=12,300+(0.06) \cdot t
  1. Identify Growth Rate: We need to find a formula that shows a 6%6\% growth each year. Since it's a percentage growth, we're dealing with exponential growth, not linear.
  2. Base Formula for Exponential Growth: The base formula for exponential growth is Initial Value ×(1+Growth Rate)t\times (1 + \text{Growth Rate})^t, where tt is the number of years after the initial year.
  3. Plug in Values: Plug in the values: Initial Value is 12,30012,300 kilowatt-hours, Growth Rate is 6%6\% or 0.060.06, and tt is the number of years after 20002000.
  4. Final Formula: The correct formula should be E(t)=12,300×(1+0.06)tE(t) = 12,300 \times (1 + 0.06)^t, which simplifies to E(t)=12,300×(1.06)tE(t) = 12,300 \times (1.06)^t.
  5. Compare Options: Comparing the options, we see that option (A) matches our formula: E(t)=12,300×(1.06)tE(t) = 12,300 \times (1.06)^t.

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