From 1990 to 2000, the number of thousand visits by people to Bryce Canyon National Park increased about 23.9 thousand visits per year. In 2000, there were 1102.4 thousand visits to the park.
Write an equation that gives the number of thousand visits as a function of the number of years since 1990.
How many visits were made to the park in 1995?
10.25
To write an equation that gives the number of thousand visits as a function of the number of years since 1990, we need to determine the initial number of visits in 1990 and the rate of increase per year.
Let's assume that the initial number of visits in 1990 is denoted by N₀, and the rate of increase per year is denoted by r.
The equation we can write to represent the number of thousand visits as a function of the number of years since 1990 is then:
N = N₀ + r * t
Where:
N is the number of thousand visits.
t is the number of years since 1990.
Given that in 2000 (which is 10 years after 1990), there were 1102.4 thousand visits to the park, we can substitute these values into the equation and solve for N₀ and r.
1102.4 = N₀ + r * 10
To determine the value of N₀ and r, we need one more data point. Let's use the information given that "from 1990 to 2000, the number of thousand visits by people to Bryce Canyon National Park increased about 23.9 thousand visits per year."
This means that the rate of increase per year (r) is 23.9.
Substituting r = 23.9 into the equation gives us:
1102.4 = N₀ + 23.9 * 10
Simplifying the equation gives:
1102.4 = N₀ + 239
Now we can solve for N₀:
N₀ = 1102.4 - 239
N₀ = 863.4
Therefore, the equation that gives the number of thousand visits as a function of the number of years since 1990 is:
N = 863.4 + 23.9 * t
To find the number of visits made to the park in 1995 (which is 5 years after 1990), we can substitute t = 5 into the equation:
N = 863.4 + 23.9 * 5
N ≈ 863.4 + 119.5
N ≈ 982.9
Therefore, approximately 982.9 thousand visits were made to the park in 1995.
To write the equation that gives the number of thousand visits as a function of the number of years since 1990, we can use the given information:
Let's define "x" as the number of years since 1990. We know that in 1990 (x=0), the number of visits was 0. We also know that from 1990 to 2000 (x=10), the number of visits increased by 23.9 thousand visits per year. Finally, in 2000 (x=10), there were 1102.4 thousand visits.
Using this information, we can write the equation:
Number of thousand visits = 0 + 23.9x
Now, to find the number of visits made to the park in 1995, we need to find the value of x when the year is 1995. Since 1995 is 5 years after 1990, we substitute x=5 into the equation:
Number of thousand visits = 0 + 23.9(5)
Simplifying the equation gives us:
Number of thousand visits = 0 + 119.5
Therefore, the number of visits made to the park in 1995 was 119.5 thousand visits.