We are asked to use the following formula to find the average movie ticket price in 1990, 2000, and 2010.
P=y^2/400+7y/100+2.96
Note that in this formula y represents the number of years since 1980, so we must subtract 1980 from the given years before we substitute the value into the formula. Let's see how this works for the year 1990.
y=1990-1980=10
To get the average ticket price in 1990, we substitute y=10 in the formula.
The ticket price for other years can be calculated similarly.
The table below contains the results.
Year
Expresssion
Ticket Price
1990
10^3/2500-10^2/100+6( 10)/25+2.62
4.42
2000
20^3/2500-20^2/100+6( 20)/25+2.62
6.62
2010
30^3/2500-30^2/100+6( 30)/25+2.62
11.62
Let's compare the ticket prices in 1990, 2000, and 2010 according to the two models.
Besides, the values let's also compare the rate of increase.
4
&$3.91& +$1.45 ⟶ &$5.36& +$1.95 ⟶ &$7.31&
&$4.42& +$2.20 ⟶ &$6.62& +$5.00 ⟶ &$11.62&
We can see that the second model not only gives higher prices, but the rate of increase of the price is also increasing.
