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Advanced Math / Nonlinear functions Difficulty: Medium

$D equals, 5,640 times, open parenthesis, 1 point 9, close parenthesis, to the t power$

The equation above estimates the global data traffic D, in terabytes, for the year that is t years after 2010. What is the best interpretation of the number 5,640 in this context?

The estimated amount of increase of data traffic, in terabytes, each year

The estimated percent increase in the data traffic, in terabytes, each year

The estimated data traffic, in terabytes, for the year that is t years after 2010

The estimated data traffic, in terabytes, in 2010

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Explanation

Choice D is correct. Since t represents the number of years after 2010, the estimated data traffic, in terabytes, in 2010 can be calculated using the given equation when $t equals 0$ . Substituting 0 for t in the given equation yields $D equals, 5,640 times, open parenthesis, 1 point 9, close parenthesis, to the 0 power$ , or $5,640 times 1, equals 5,640$ . Thus, 5,640 represents the estimated data traffic, in terabytes, in 2010.

Choice A is incorrect. Since the equation is exponential, the amount of increase of data traffic each year isn’t constant. Choice B is incorrect. According to the equation, the percent increase in data traffic each year is 90%. Choice C is incorrect. The estimated data traffic, in terabytes, for the year that is t years after 2010 is represented by D, not the number 5,640.