Question

You and your family take a summer vacation to Ireland. You discover that the number of Americans visiting Ireland is increasing by \(80,000\) visitors per year. Let \(x\) represent the number of visitors in 1997 . Write an expression for the number of visitors in 2000 .

Short answer

The expression representing the number of visitors in 2000 is \(y = 240000 + x\).

Step-by-step solution

Understanding the problem

We know that the number of Americans visiting Ireland increases by 80,000 each year. If \(x\) represents the number of visitors in 1997, we want to find an expression that represents the number of visitors in the year 2000.

Determining the difference in years

We want to find the number of visitors in 2000 while we know the number of visitors in 1997. So, we subtract the initial year from the final year to get the difference. That would be 2000 - 1997 = 3. So there are 3 years between 1997 and 2000.

Using linear growth formula

We can use the formula for a linear function, which looks like \(y = mx + b\). Here, 'm' is the rate of increase, 'x' is the time (here, number of years), and 'b' is the initial quantity (here, visitors in 1997). Here, 'm' is the rate of increase in visitors per year, which is 80,000. 'x' is the difference in a number of years, which we found out to be 3. 'b' is the number of visitors in 1997, represented by \(x\).

Construct the expression

Now, just plug in the values into the equation. So we get \(y = 80000 * 3 + x\), which simplifies to \(y = 240000 + x\). Therefore, the number of visitors in 2000 can be represented by the expression \(240000 + x\).