from 1990 to 2000, the number of thousand visits by people to hawaii volcanoes national park increased by about 43.1 thousand visits. per year. In 2000, there were about 1529.6 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.

To write an 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 denote the number of years since 1990 as "x". We are given that from 1990 to 2000 (which is a span of 10 years), the number of thousand visits increased by about 43.1 thousand visits per year. This means that for each year, the number of thousand visits increased by 43.1.

In 1990, the number of thousand visits was not provided, but we know that in 2000, there were about 1529.6 thousand visits. So, we can assume that in 1990, the number of thousand visits was 1529.6 minus the increase over the 10 years, which is 1529.6 - (43.1 * 10).

So, our equation to represent the number of thousand visits as a function of the number of years since 1990 is:

Number of thousand visits = (43.1 * x) + (1529.6 - (43.1 * 10))

Simplifying further, the equation becomes:

Number of thousand visits = 43.1x + 1500.5

Thus, the equation that gives the number of thousand visits as a function of the number of years since 1990 is 43.1x + 1500.5.

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 information provided.

Let's define the number of years since 1990 as "x" and the number of thousand visits as "y".

According to the information given, from 1990 to 2000 (in 10 years), the number of thousand visits increased by about 43.1 thousand visits per year.

Therefore, we can calculate the initial number of thousand visits in 1990 by subtracting 43.1 thousand visits per year for each year from 2000 to 1990.

y = 1529.6 - (43.1 * (x - 1990))

So, the equation that gives the number of thousand visits as a function of the number of years since 1990 is y = 1529.6 - (43.1 * (x - 1990)).

Let n be the thousands of visitors

Let x be the number of years since 1990

n(x) then produces the number of visitors in any given year since 1990. We are told that in 2000 (10 years after 1990)

n(10) = 1529.6
n(x+10) = 1529.6 + 43.1x

That gives us the visitors for years after 2000. But we want to back up to 1990. SO substitute (x-10) for x to get

n(x-10+10) = 1529.6 + 43.1(x-10)
n(x) = 1529.6 + 43.1x - 431
n(x) = 1098.6 + 43.1x

Makes sense, since during the first 10 years, 431 visitors are added, making the count 1529.6 in 2000. And things just keep going from there.