The annual number of visitors to a museum is shown in the figure.

Question

If xequals0 represents​ 1970, xequals5 represents​ 1975, the yearly number of visitors can be approximated by yequals1.31xplus3.19​, where y is in thousands.
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Part 1
Use the equation to approximate the number of visitors in 1990.
Part 2
In 1990​, the museum received approximately
  
enter your response here thousand visitors.
​(Simplify your answer. Type an integer or a decimal. Round to the nearest hundredth if​ needed.)

Answer 1

To find the approximate number of visitors to the museum in 1990, we first need to determine the value of \( x \) for that year. Since \( x = 0 \) represents 1970 and \( x = 5 \) represents 1975, we can calculate \( x \) for 1990.

We see that 1990 is 20 years after 1970, so:

1. \( 1990 - 1970 = 20 \)
2. In 5 years (from 1970 to 1975), \( x \) increases by 5. So:
   • From 1970 to 1990 (20 years), we can scale appropriately:

\[ x = 20 / 5 \times 5 = 20 \] Thus, \( x \) will be 20 (or simply counting, from 1970 to 1990: include 1970 as 0, 1975 as 5, 1980 as 10, 1985 as 15, and 1990 as 20).

Next, we plug \( x = 20 \) into the equation \( y = 1.31x + 3.19 \):

\[ y = 1.31(20) + 3.19 \]

Calculating this gives:

\[ y = 26.2 + 3.19 = 29.39 \]

Thus, the approximate number of visitors in 1990 (in thousands) is:

\[ 29.39 \]

Now, addressing Part 2:

In 1990, the museum received approximately 29.39 thousand visitors.