Q12. - Algebra 2

Question

The number of cable TV systems after 1985 can be modeled by the function $C\left(t\right)=-43.2t^2+1343t+790$, where (t) represents the number of years since 1985. What trends in cable TV subscriptions does the graph suggest ?

Step-by-Step Solution

Answer

The number of cable TV in between $t=0 \text{and }t=15$ rose steadily and afterwards starts declining. It means that the cable TV subscriptions rose from the year 1985 to 2000 steadily. And it can also be interpreted that after 2000 the number of cable TV subscriptions will fall steadily such that they tend to zero which is not practically possible in near future. Hence there is not any reason to believe that the cable TV subscriptions will fall below level zero.

Step 1. Write down the given information.

The number of cable TV systems are modeled by the function $C\left(t\right)=-43.2t^2+1343t+790$, where (t) represents the number of years since 1985.

Step 2. Sketch the graph of given equation.

The graph of the equation $C\left(t\right)=-43.2t^2+1343t+790$ from the year 1985 to 2005 is shown below, where (t) represents the number of years since 1985.

Step 3. Interpretation from the graph.

From the graph of the equation, it can be interpreted that the number of cable TV in between $t=0 \text{and }t=15$ rose steadily and afterwards starts declining. It means that the cable TV subscriptions rose from the year 1985 to 2000 steadily. And it can also be interpreted that after 2000 the number of cable TV subscriptions will fall steadily such that they tend to zero which is not practically possible in near future. Hence there is not any reason to believe that the cable TV subscriptions will fall below level zero.

Step 4. Conclusion.

The number of cable TV in between $t=0 \text{and }t=15$ rose steadily and afterwards starts declining. It means that the cable TV subscriptions rose from the year 1985 to 2000 steadily. And it can also be interpreted that after 2000 the number of cable TV subscriptions will fall steadily such that they tend to zero which is not practically possible in near future. Hence there is not any reason to believe that the cable TV subscriptions will fall below level zero.