Question

The total numbers N (in thousands ) of overnight stays at Zion National Park x years after 2000 can be modeled by N=-0.032x³+0.73x²+2.2x+248 where 0<=x<=18. Find N(10).

Answer 1

To find N(10), the number of overnight stays at Zion National Park 10 years after 2000, we substitute x = 10 into the model and calculate the result to be 311,000 overnight stays.

Step-by-step explanation:

To find N(10), which represents the number of overnight stays at Zion National Park 10 years after 2000, we substitute x = 10 into the given model N = -0.032x³ + 0.73x² + 2.2x + 248.

First we calculate the cubic term:

-0.032 × (10)³ = -0.032 × 1000 = -32

Next the square term:
0.73 × (10)² = 0.73 × 100 = 73

Now the linear term:
2.2 × 10 = 22

Adding these values to the constant term:

N(10) = -32 + 73 + 22 + 248

N(10) = 311 (in thousands of overnight stays)

Therefore, there were 311,000 overnight stays at Zion National Park in the year 2010.