Final answer:
The correct equation to represent the virus spreading in Sunnyville is y = 200(0.84)², which reflects the rate of spread as 16% per day for two days.
Step-by-step explanation:
The student is asking which equation correctly represents a scenario where a virus is spreading around Sunnyville. Given the initial number of infected people is 200, and the infection is spreading at a rate of 16% each day over 2 days, we are looking for the equation that accounts for exponential growth. An increase of 16% each day means the number of people infected would be 116% (or 1.16 times) the previous day's infected population. However, we can deduct the 16% from 100% to work out what percentage remains unaffected each day, yielding 84% or 0.84. Therefore, after two days, the equation will involve raising 0.84 to the power of 2, multiplied by the initial infected number, 200.
The correct equation to represent the situation after two days is y = 200(0.84)². The answer choices can be analyzed as follows:
- Option A, y = 200(0.84)², is correct because it considers a reduction to 0.84 of the initial quantity each day for 2 days.
- Option B, y = 200(0.16)², is incorrect because it uses the rate of spread as the multiplier rather than the remaining percentage of a non-infected proportion.
- Option C, y = (0.84 * 200)², is incorrect because it squares the initial population after a single day's growth, not accounting for two days.
- Option D, y = 0.84(200)², is incorrect because it squares the initial population before applying the daily growth, which does not represent the growth over two days.