Question

The amount of money that a movie makes in ticket sales is called its box office gross. The box office gross, in millions of dollars, of a particular movie each week is shown in the table. The amounts have been rounded to the nearest hundred thousand.

Week box office gross ($ millions)
1 1.2
3 6.8
5 10.2
6 10.7
7 10.3
9 6.3

An executive for the movie production company wants to create a function that models this data

Create a function that can be used to model the data shown in the table. Be sure to define the variables and provide justification for your choice of function.

A. The functionta is G(t)=-0.408225t²+4.76597t-3.34866 , where G is the box office gross in millions earned and t is the time in weeks.
B. The function that can model the data is G(t)=3.34866t²-4.76597t+0.408225 where G is the box office gross in millions earned and tis the time in weeks.
C. The function that can model the data is G(t)=-3.34866t²+4.76597t-0.408225 , where G is the box office gross in millions earned and t is the time in weeks.
D. The function that can model the data is G(t)=0.408225t²-4.76597t+3.34866 , where G is the box office gross in millions earned and t is the time in weeks.

Answer 1

The correct mathematical function to model the box office gross based on the provided data cannot be determined without further analysis. The data suggests a non-linear trend likely captured by a quadratic function; a negative leading coefficient is plausible given typical box office trends.

option a is the correct

Step-by-step explanation:

The question involves creating a function to model the box office gross of a movie over different weeks. Given the data in the table, we need to construct a mathematical function that represents the gross earnings (G) as a function of time in weeks (t). In the context of this scenario, we would typically seek a polynomial function since the earnings demonstrate a non-linear trend that a polynomial could potentially capture well.

The coefficients of this function will be determined by fitting the function to the provided data points. Typically, this is performed using statistical techniques such as regression analysis, which are beyond the high school level curriculum.

It is also worth noting that the correct option for the provided parameters isn't included, suggesting that the student might need to use techniques like least squares regression to find the parameters that best fit the data.

To accurately choose between options A, B, C, and D, actual computation or analysis would need to be done using the given data points, which isn't possible in this format.

Therefore, we cannot select the correct function without additional analysis. However, from general observation, a movie's box office gross tends to start low, increase to a peak, and then decrease as interest wanes, which suggests that the leading coefficient of a quadratic function would be negative, which would make options A or C more likely if we were to guess based on typical box office trends.