Functions in Context Worksheets Grade 9

1. The function P(t) = 1200(1.08)^t models the population of Kaia's town over t years. What does P(9) represent?
2. A drone is flying over a field following a parabolic path modeled by the function h(t) = -2t² + 12t + 5, where h represents the drone's height in meters and t represents time in seconds. At what time does the drone reach its maximum height?
3. Hana is analyzing the water depth in a tidal pool. The depth, in meters, is modeled by the function f(t) = 4sin(πt/6) + 6, where t is the time in hours after midnight. A graph of this function is drawn on a coordinate plane, with t on the horizontal axis and f(t) on the vertical axis. What is the interpretation of the maximum value of f(t) in this context?

…and 5 more problems

1. Hana is tracking the height of a model rocket launched from the ground. The rocket's height in meters, h(t), after t seconds is modeled by the function h(t) = -4t² + 32t. Interpret the meaning of h(4) in the context of this problem and calculate its value.
2. Liam is designing a parabolic arch for a bridge. The arch's height above the ground is modeled by the function h(x) = -0.02x² + 1.2x, where x is the horizontal distance in meters from the left support and h(x) is the height in meters. What is the maximum height of the arch above the ground?
3. Mere is analyzing the graph of a quadratic function that models the height (in meters) of a soccer ball kicked from the ground. The function is h(t) = -5t^2 + 20t, where t is time in seconds. The graph is a parabola opening downward, crossing the t-axis at t = 0 and t = 4. What does the vertex of this parabola represent in the context of the soccer ball's flight?

…and 3 more problems

1. The height of a plant is modeled by h(t) = 15 + 0.8t, where t is days and h is cm. What does h(12) represent?
2. The population of a certain species of birds in a wildlife reserve is modeled by the function P(t) = 1200/(1 + 3e^(-0.2t)), where t is the number of years since monitoring began and P(t) is the population size. According to this model, what is the maximum carrying capacity (in number of birds) that the reserve can support?
3. Aroha is tracking the temperature of a chemical reaction over time. The temperature T(t) in degrees Celsius after t minutes is modeled by the quadratic function T(t) = -2t² + 24t + 10. Interpret the meaning of T(6) in the context of this reaction and determine its value.

…and 3 more problems