$\"\"$

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The average price for a movie ticket can be represented by $\"\"$ .

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Where $\"\"$ is the number of years since $\"\"$ .

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a.

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Find the average price of a ticket in $\"\"$ and $\"\"$ .

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Case(i): $\"\"$ .

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$\"\"$ (Formula for average price for a movie ticket)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Evaluate powers)

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$\"\"$ (Simplify)

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$\"\"$ (Add: $\"\"$ )

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Case(ii): $\"\"$ .

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$\"\"$ (Formula for average price for a movie ticket)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Evaluate powers)

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$\"\"$ (Simplify)

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$\"\"$ (Add: $\"\"$ )

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Case(iii): $\"\"$ .

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$\"\"$ (Formula for average price for a movie ticket)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Evaluate powers)

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$\"\"$ (Simplify)

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$\"\"$ (Add: $\"\"$ )

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Therefore, the average price for a movie tickets are $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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b. \ \ Another equation that can be used to represent ticket prices is $\"\"$ .

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Find the price of a ticket in $\"\"$ and $\"\"$ .

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Case(i): $\"\"$ .

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$\"\"$ (Formula for average price for a movie ticket)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Evaluate powers)

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$\"\"$ (Simplify)

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$\"\"$ (Add: $\"\"$ )

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Case(ii): $\"\"$ .

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$\"\"$ (Formula for average price for a movie ticket)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Evaluate powers)

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$\"\"$ (Simplify)

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$\"\"$ (Add: $\"\"$ )

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Case(iii): $\"\"$ .

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$\"\"$ (Formula for average price for a movie ticket)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Evaluate powers)

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$\"\"$ (Simplify)

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$\"\"$ (Add: $\"\"$ )

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Therefore, the average price for a movie tickets are $\"\"$ , $\"\"$ and $\"\"$ .

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Hence, the average price is higher when compared to average prices in part (a).

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The average prices found in part (a) become increasingly higher with time.

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$\"\"$

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a. The average price for a movie tickets are $\"\"$ , $\"\"$ and $\"\"$ .

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b. The average price for a movie tickets are $\"\"$ , $\"\"$ and $\"\"$ .