The expression 1.5*1.09^(t) models the housing costs, in thousands of dollars, for summer term t years since Chinedu applied to his college. What does 1.09 represent in this expression? Choose 1 answer: (A) Chinedu applied to his school 9 years ago. (B) The summer housing costs were $1,090 the year that Chinedu applied to his college. (C) The summer housing costs increase by 9% each year.

Question

The expression  1.5*1.09^(t) models the housing costs, in thousands of dollars, for summer term  t years since Chinedu applied to his college. What does 1.09 represent in this expression? Choose 1 answer: (A) Chinedu applied to his school 9 years ago. (B) The summer housing costs were  $1,090 the year that Chinedu applied to his college. (C) The summer housing costs increase by  9% each year.

Bytelearn · Accepted Answer

Understand Structure: Understand the structure of the expression. The expression given is 1.5*1.09^(t), which is a mathematical model for housing costs. The base number 1.09 is raised to the power of t, where t represents the number of years since Chinedu applied to his college.Identify Role: Identify the role of 1.09 in the expression. In the context of the expression, 1.09 is the factor by which the initial housing costs (represented by 1.5 thousand dollars) are multiplied each year. This suggests that it is a growth factor for the housing costs.Relate Growth Factor: Relate the growth factor to the percentage increase. A growth factor of 1.09 indicates that the housing costs increase by 9% each year. This is because a 100% increase would be represented by a factor of 2 (doubling the cost), and a 9% increase is represented by 1 + 0.09, which equals 1.09.Match Correct Answer: Match the growth factor to the correct answer choice. Given that a growth factor of 1.09 represents a 9% annual increase in housing costs, we can conclude that the correct answer is (C) The summer housing costs increase by 9% each year.

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