Question

The percent of US. households with high speed intemet h can be estimnted by h=-02n²+72n+1.5, where n is the number of years since 1990. Use the Quadratic Formulo to determine when 20% of the populotion will hove high speed lintemet.

Answer 1

To find when 20% of the U.S. population will have high-speed internet, we solve the quadratic equation -0.2n² + 72n + 1.5, setting has 20. We use the Quadratic Formula to obtain the value of n, which represents the years since 1990 and then add this to 1990 to get the specific year.

Step-by-step explanation:

When will 20% of the population have high-speed internet can be determined by solving the quadratic equation h=-0.2n²+72n+1.5 where h represents the percentage of U.S. households with high-speed internet and n is the number of years since 1990. We set h equal to 20 and solve for n using the Quadratic Formula.

20 = -0.2n² + 72n + 1.5

We first move all terms to one side to get the standard form of the quadratic equation:

0 = -0.2n² + 72n - 18.5

The Quadratic Formula is n = (-b ± √(b² - 4ac)) / (2a). Plugging in the values, we obtain two possible solutions for n. We will consider only the positive, realistic year since 1990. Then we calculate the interested year by adding the value of n to 1990.