Question

The polynomial−7.5x 2+113x+2019 models the yearly number of visitors (in thousands) x years after 2006 to a park. Use this polynomial to estimate the number of visitors to the park in 2018.

a) 1,200 visitors
b) 1,500 visitors
c) 1,800 visitors
d) 2,000 visitors

Answer 1

To estimate the visitors in 2018, we substitute x=12 into the polynomial −7.5x² + 113x + 2019, resulting in 2,295,000 visitors. The closest given option is 2,000 visitors (in thousands).

Step-by-step explanation:

To estimate the number of visitors to the park in 2018 using the given polynomial −7.5x² + 113x + 2019, we first calculate the number of years after 2006. The year 2018 is 12 years after 2006, so we let x = 12. Substituting x into the polynomial:

−7.5(12)² + 113(12) + 2019 = −7.5(144) + 1356 + 2019 = − 1080 + 1356 + 2019

Calculating this gives 2295 (in thousands), which means there were 2,295,000 visitors in 2018. Since the options are given in thousands, we choose the closest option, which is 2,000 visitors (in thousands).