Question

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Explanation:

To solve this, we analyze the function \( f(t) \), where \( t \) is years after 1950, and \( f(t) \) is the number of vinyl records sold. We need to find \( t \) for each sales number and match the equations.

Step 1: Analyze "91,299 vinyl records were sold in 19__"

1950 + \( t \) = year. We need \( f(t) = 91,299 \). From the tiles, \( f(11) = 91,299 \). So \( t = 11 \), year = 1950 + 11 = 1961.
Match: \( f(11) = 91,299 \)

Step 2: Analyze "68,594 vinyl records were sold in 1958"

Year = 1958, so \( t = 1958 - 1950 = 8 \). We need \( f(8) = 68,594 \).
Match: \( f(8) = 68,594 \)

Step 3: Analyze "38,720 vinyl records were sold in 1952"

Year = 1952, so \( t = 1952 - 1950 = 2 \). We need \( f(2) = 38,720 \).
Match: \( f(2) = 38,720 \)

Step 4: Analyze "161,743 vinyl records were sold in 1967"

Year = 1967, so \( t = 1967 - 1950 = 17 \). We need \( f(17) = 161,743 \).
Match: \( f(17) = 161,743 \)

Final Matches:

• 91,299 vinyl records were sold in 1961: \( \boldsymbol{f(11) = 91,299} \)
• 68,594 vinyl records were sold in 1958: \( \boldsymbol{f(8) = 68,594} \)
• 38,720 vinyl records were sold in 1952: \( \boldsymbol{f(2) = 38,720} \)
• 161,743 vinyl records were sold in 1967: \( \boldsymbol{f(17) = 161,743} \)

Answer:

To solve this, we analyze the function \( f(t) \), where \( t \) is years after 1950, and \( f(t) \) is the number of vinyl records sold. We need to find \( t \) for each sales number and match the equations.

Step 1: Analyze "91,299 vinyl records were sold in 19__"

1950 + \( t \) = year. We need \( f(t) = 91,299 \). From the tiles, \( f(11) = 91,299 \). So \( t = 11 \), year = 1950 + 11 = 1961.
Match: \( f(11) = 91,299 \)

Step 2: Analyze "68,594 vinyl records were sold in 1958"

Year = 1958, so \( t = 1958 - 1950 = 8 \). We need \( f(8) = 68,594 \).
Match: \( f(8) = 68,594 \)

Step 3: Analyze "38,720 vinyl records were sold in 1952"

Year = 1952, so \( t = 1952 - 1950 = 2 \). We need \( f(2) = 38,720 \).
Match: \( f(2) = 38,720 \)

Step 4: Analyze "161,743 vinyl records were sold in 1967"

Year = 1967, so \( t = 1967 - 1950 = 17 \). We need \( f(17) = 161,743 \).
Match: \( f(17) = 161,743 \)

Final Matches:

• 91,299 vinyl records were sold in 1961: \( \boldsymbol{f(11) = 91,299} \)
• 68,594 vinyl records were sold in 1958: \( \boldsymbol{f(8) = 68,594} \)
• 38,720 vinyl records were sold in 1952: \( \boldsymbol{f(2) = 38,720} \)
• 161,743 vinyl records were sold in 1967: \( \boldsymbol{f(17) = 161,743} \)