Question

The quadratic regression equation for AQI (Air Quality Index) over time is given as n = 1.76t^2 - 13.32t + 41.00, where n is the number of days the AQI exceeded 100 and t represents years since 1990. Estimate the days AQI exceeded 100 in 2002. a) 281 days b) 97 days c) 135 days d) 52 days

Answer 1

The estimated number of days the AQI exceeded 100 in 2002 is 281 days.

Step-by-step explanation:

To estimate the number of days the AQI exceeded 100 in 2002, substitute t = 12 into the equation n = 1.76t^2 - 13.32t + 41.00.

n = 1.76(12)^2 - 13.32(12) + 41.00 = 281

Therefore, the estimated number of days the AQI exceeded 100 in 2002 is 281 days.

Answer 2

To estimate the days the Air Quality Index exceeded 100 in 2002, we substitute t=12 into the quadratic equation, resulting in approximately 135 days, which corresponds to option (c).

Step-by-step explanation:

The student has provided the quadratic regression equation n = 1.76t^2 - 13.32t + 41.00, where n represents the days the Air Quality Index (AQI) exceeded 100 and t represents the years since 1990. To estimate the number of days AQI exceeded 100 in 2002, we need to calculate the value of n for t = 12 (since 2002 is 12 years after 1990).

Replacing t with 12 in the equation, we get:

n = 1.76(12)^2 - 13.32(12) + 41.00

n = 1.76(144) - 159.84 + 41.00

n = 253.44 - 159.84 + 41.00

n = 134.60

Therefore, the estimated number of days AQI exceeded 100 in 2002 is approximately 135 days, which closely matches option (c).