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The mean annaul salary of an NBA player,...

The mean annaul salary of an NBA player, S, can be estimated using the equation `S=161,400(1.169)^(t)`, where S is measured in thousands of dollars, and t represents the number of yearts since 1980 for `0letle20`. Which of the following statements is the best interpretation of 161,400 in the context of this problem?

A

The estimated mean annual salary, in dollars, of an NBA player in 1980.

B

The estimated mean annual salary, in dollars, of an NBA player in 2000.

C

The estimated yearly increase in the mean annual salary of an NBA player.

D

The estimated yearly decrease in the mean annual salary of an NBA player.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to interpret the constant value 161,400 in the equation for the mean annual salary of an NBA player, given by: \[ S = 161,400(1.169)^t \] where \( S \) is measured in thousands of dollars and \( t \) represents the number of years since 1980. ### Step-by-Step Solution: 1. **Understand the Equation**: The equation shows that the salary \( S \) depends on the variable \( t \), which counts the years since 1980. The term \( 1.169^t \) indicates that the salary increases exponentially over the years. 2. **Substitute \( t = 0 \)**: To find the value of \( S \) at the starting point (the year 1980), we substitute \( t = 0 \) into the equation: \[ S = 161,400(1.169)^0 \] 3. **Calculate \( (1.169)^0 \)**: Since any number raised to the power of 0 is 1, we have: \[ S = 161,400 \times 1 = 161,400 \] 4. **Interpret the Result**: The value of \( S \) when \( t = 0 \) (the year 1980) is 161,400. This means that the estimated mean annual salary of an NBA player in the year 1980 is $161,400,000 (since \( S \) is in thousands of dollars). 5. **Choose the Correct Interpretation**: Among the options provided, the best interpretation of the value 161,400 is: - "Estimated mean annual salary in dollars of an NBA player in 1980." ### Conclusion: The correct answer is option A: "Estimated mean annual salary in dollars of an NBA player in 1980."
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