Function Parameters Worksheets Grade 9

1. A research lab is studying bacterial growth in a petri dish. The initial bacterial population is 500. The population doubles every 3 hours. Write an exponential function P(t) that models the bacterial population after t hours, and determine how many bacteria will be present after 12 hours.
2. Noah is analyzing the depreciation of a piece of machinery. Its value, in dollars, after x years is modeled by the exponential function V(x) = 8400(0.85)^x. A graph of this function shows the value decreasing over time, starting from a point on the vertical axis at x=0 and curving downward to approach zero. What is the real-world meaning of the number 8400 in this model, and what does the number 0.85 represent?
3. y = 27(1.02)^x models Isabella's savings account. What does 27 represent? What does 1.02 represent?

…and 4 more problems

1. A graph (described below) shows the decay of a radioactive isotope over time. The y-axis represents the mass in grams, and the x-axis represents time in years. The curve passes through the points (0, 81) and (3, 27). The function is of the form y = a(b^x). What is the value of b, and what does it represent in the context of this decay?
2. Emma is studying the growth of a bacteria culture. She models the number of bacteria after x hours using the exponential function y = 150(1.25)^x. On a coordinate grid, she plots points for x = 0, 1, 2, 3, and 4. Describe what the number 150 and the number 1.25 represent in the context of the bacteria growth.
3. The graph below (described in text) shows the value of a rare comic book over time. The value V (in dollars) is modeled by the exponential function V(t) = 75(1.05)^t, where t is the number of years since 2010. A coordinate plane is drawn with the horizontal axis labeled 'Years since 2010 (t)' and the vertical axis labeled 'Value (V) in dollars'. The curve starts at (0, 75) and rises slowly, passing through points such as (10, approximately 122) and (20, approximately 199). Interpret the meaning of the parameters 75 and 1.05 in the context of the comic book's value.

…and 4 more problems

1. Matiu is studying the growth of a bacteria colony. The number of bacteria after t hours is modeled by the exponential function B(t) = 400(1.08)^t. The graph of this function is shown on a coordinate plane, with the horizontal axis labeled 'Time (hours)' and the vertical axis labeled 'Number of Bacteria'. Interpret the meaning of the parameters 400 and 1.08 in the context of the bacteria colony.
2. Tane's investment grows according to y = 8200(1.07)^x, where y is the value after x years. What does 8200 represent? What does 1.07 represent?
3. Liam is studying bacterial growth in his biology class. He observes that a bacterial culture starts with 200 cells and doubles every 3 hours. Write an exponential function in the form f(t) = a * b^t that models the number of bacteria after t hours, then determine how many bacteria will be present after 12 hours.

…and 3 more problems