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Karim sent a chain email to 10 of his friends. The number of people who got the email increases by a factor of 1.4 every week. Which expression gives the number of people who got the email after 6 weeks? Choose 1 answer: (A) 10+1.4*6 (B) 10*1.4^(6) (C) (10*1.4)^(6) (D) (10+1.4)*6

Karim sent a chain email to 1010 of his friends. The number of people who got the email increases by a factor of 11.44 every week.\newlineWhich expression gives the number of people who got the email after 66 weeks?\newlineChoose 11 answer:\newline(A) 10+1.4⋅6 10+1.4 \cdot 6 \newline(B) 10⋅1.46 10 \cdot 1.4^{6} \newline(C) (10⋅1.4)6 (10 \cdot 1.4)^{6} \newline(D) (10+1.4)⋅6 (10+1.4) \cdot 6

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Q. Karim sent a chain email to 1010 of his friends. The number of people who got the email increases by a factor of 11.44 every week.\newlineWhich expression gives the number of people who got the email after 66 weeks?\newlineChoose 11 answer:\newline(A) 10+1.4⋅6 10+1.4 \cdot 6 \newline(B) 10⋅1.46 10 \cdot 1.4^{6} \newline(C) (10⋅1.4)6 (10 \cdot 1.4)^{6} \newline(D) (10+1.4)⋅6 (10+1.4) \cdot 6
  1. Problem Understanding: Understand the problem.\newlineWe need to find the expression that represents the number of people who received the email after 66 weeks, given that the number of people increases by a factor of 1.41.4 each week, starting with 1010 people.
  2. Analyzing Answer Choices: Analyze the answer choices.\newline(A) 10+1.4×610+1.4\times 6 suggests a linear increase.\newline(B) 10×1.4610\times 1.4^{6} suggests an initial value of 1010 people increasing by a factor of 1.41.4 each week for 66 weeks.\newline(C) (10×1.4)6(10\times 1.4)^{6} suggests taking the product of 1010 and 1.41.4 and then raising it to the power of 66, which would be incorrect as it implies compounding the initial number of people with the factor each week before raising to the power of 66.\newline(D) 10×1.4610\times 1.4^{6}00 suggests a linear increase with an incorrect initial value.
  3. Identifying Growth Type: Identify the correct type of growth.\newlineThe problem states that the number of people increases by a factor of 1.41.4 every week. This is exponential growth, not linear growth. Therefore, options (A)(A) and (D)(D) can be eliminated because they suggest linear growth.
  4. Choosing Correct Expression: Choose the correct expression for exponential growth.\newlineThe correct expression for exponential growth is the initial value multiplied by the growth factor raised to the power of the number of time periods. In this case, the initial value is 1010, the growth factor is 1.41.4, and the number of weeks is 66. Therefore, the correct expression is 10×1.4610 \times 1.4^{6}, which corresponds to option (B).

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