The number of nano-related patents that are granted in the US increases by a factor of 1.2 every year. In 1991 , there were 60 nano-related patents. Which expression gives the number of patents in 1998? Choose 1 answer: (A) 60+(1+1.2)^(7) (B) 60*1.2^(7) (C) 60+1.2^(7) (D) 60*(1+1.2)^(7)

Question

The number of nano-related patents that are granted in the US increases by a factor of 1.2 every year. In 1991 , there were 60 nano-related patents. Which expression gives the number of patents in  1998? Choose 1 answer: (A)  60+(1+1.2)^(7) (B)  60*1.2^(7) (C)  60+1.2^(7) (D)  60*(1+1.2)^(7)

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. We need to find the expression that represents the growth of the number of patents from 1991 to 1998. The growth is exponential, with a factor of 1.2 each year.Calculate years: Calculate the number of years from 1991 to 1998. 1998 - 1991 = 7 yearsApply growth formula: Apply the exponential growth formula. The number of patents in a given year is the initial number of patents multiplied by the growth factor raised to the number of years that have passed. Number of patents = Initial patents * (Growth factor)^(Number of years)Substitute values: Substitute the given values into the formula. Initial patents = 60 Growth factor = 1.2 Number of years = 7 Number of patents = 60 * (1.2)^(7)Identify correct expression: Identify the correct expression from the choices. The correct expression that matches our formula is (B) 60*1.2^(7).

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