Question

for this item, complete the choice matrix by clicking the appropriate answer in each row.
complete the choice matrix by selecting the best description for each scenario.
a basketball tournament has 0.5 times the number of teams in each successive round.
a corporations revenue drops 10%, 9%, and 4% in 3 consecutive months.
the membership of a club goes up by 3% each year.
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Explanation:

Step1: Analyze the first scenario

For the basketball tournament, if the number of teams is \(0.5\) times the previous round each time, it follows the form \(y = a(0.5)^x\) (where \(a\) is the initial number of teams and \(x\) is the number of rounds). Since \(0<0.5 < 1\), this is exponential decay.

Step2: Analyze the second scenario

For the corporation's revenue, if it drops by different percentages (\(10\%\), \(9\%\), \(4\%\)) each month, it does not follow the form \(y=a(1 + r)^x\) or \(y=a(1 - r)^x\) (where \(r\) is a constant rate). So it is neither exponential growth nor decay.

Step3: Analyze the third scenario

For the club membership, if it goes up by \(3\%\) each year, it follows the form \(y=a(1 + 0.03)^x\) (where \(a\) is the initial membership and \(x\) is the number of years). Since \(1+0.03>1\), this is exponential growth.

Answer:

1. Exponential Decay
2. Neither
3. Exponential Growth