Exploring Asymptotic Behavior in Real-Life Functions

A car's fuel efficiency can be modeled by the function f(x) = 100/(x + 2), where x is the speed in miles per hour. Analyze the asymptotic behavior of this function as speed increases. What happens to the fuel efficiency?

• As speed increases, fuel efficiency increases indefinitely.

• As speed increases, fuel efficiency approaches zero.

• Fuel efficiency remains constant regardless of speed.

• As speed increases, fuel efficiency becomes negative.

A company's profit can be represented by the function P(x) = (200x)/(x + 50), where x is the number of units sold. Determine the profit when 100 units are sold and analyze the asymptotic behavior as sales increase.

• 200.00

• 133.33

• 150.00

• 100.00

The height of a water tank can be modeled by the function h(t) = 500/(t + 5), where t is time in hours. What is the height of the water tank after 10 hours? Discuss the asymptotic behavior of the height as time goes on.

• 100

• 10

• 50

• 33.33

A recipe calls for a mixture of two ingredients in the ratio given by the function R(x) = 3x/(x + 4), where x is the amount of the first ingredient in cups. If you use 8 cups of the first ingredient, what is the ratio? Analyze the behavior of the ratio as the amount of the first ingredient increases.

• 1:2

• 3:2

• 2:1

• 4:1

The speed of a rocket can be modeled by the function S(t) = 300/(t + 1), where t is time in seconds. Calculate the speed of the rocket after 5 seconds and discuss the asymptotic behavior as time increases.

• 50

• 75

• 100

• 25

A business's revenue can be modeled by the function R(x) = (50x)/(x + 10), where x is the number of products sold. What is the revenue when 20 products are sold? Analyze the asymptotic behavior of revenue as sales increase.

• 40.00

• 33.33

• 25.00

• 15.00

The volume of a gas in a container can be modeled by V(p) = 200/(p + 1), where p is the pressure in atmospheres. What is the volume when the pressure is 3 atmospheres? Discuss the asymptotic behavior of the volume as pressure increases.

• 100

• 75

• 50

• 25

A swimming pool is being filled at a rate modeled by the function F(t) = 100/(t + 2), where t is time in hours. How much water is in the pool after 4 hours? Analyze the asymptotic behavior of the water level as time goes on.

• 20

• 16.67

• 25

• 10.5

The cost of producing x items can be modeled by C(x) = (1000)/(x + 5). What is the cost when producing 15 items? Discuss the asymptotic behavior of the cost as production increases.

• 25

• 75

• 50

• 100

A population of bacteria can be modeled by the function B(t) = 500/(t + 1), where t is time in hours. What is the population after 2 hours? Analyze the asymptotic behavior of the population as time increases.

• 300

• 200

• 166.67

• 100