Function Parameters Worksheets Grade 9

1. 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.
2. Emma is analyzing the growth of two different investments. Investment A is modeled by the function A(t) = 125(1.07)^t, where A(t) represents the value in dollars after t years. Investment B is modeled by the function B(t) = 75t + 200, where B(t) also represents the value in dollars after t years. Interpret the meaning of the parameters 125 and 1.07 in Investment A, and the parameters 75 and 200 in Investment B. Which investment will have a higher value after 10 years?
3. A right circular cone has a height of 12 cm and a base radius of 5 cm. A smaller cone is formed by cutting parallel to the base, creating a cross-section at a height of 4 cm from the vertex. What is the radius of this smaller cross-section?

…and 4 more problems

1. The graph below (described in text) shows a line and an exponential curve on the same coordinate axes. The line passes through the points (0, 24) and (6, 0). The exponential curve passes through (0, 3) and (2, 12). (a) Write the equation of the line in the form y = mx + b. Then interpret the meaning of the slope m and the y-intercept b in the context of a scenario where the line models the decreasing height (in cm) of a burning candle over time x (in hours). (b) Write the equation of the exponential curve in the form y = a * b^x. Then interpret the meaning of the parameters a and b in the context of a scenario where the curve models the number of bacteria in a petri dish over time x (in hours).
2. Emma is analyzing two different investment options. Option A is modeled by the linear function A(t) = 375t + 1500, where A(t) represents the total value in dollars after t years. Option B is modeled by the exponential function B(t) = 1500(1.07)^t, where B(t) represents the total value in dollars after t years. For each function, interpret the meaning of the numerical parameters (the coefficients and constants) in the context of Emma's investments. Specifically, what does the 1500 represent in both functions, what does the 375 represent in Option A, and what does the 1.07 represent in Option B?
3. Sophia's car depreciates according to the model y = 16000(0.91)^x, where y is the car's value after x years. What does 16000 represent? What does 0.91 represent?

…and 3 more problems

1. Hana is a conservation scientist tracking the population of a rare bird species on a remote island. The number of birds, N(t), can be modeled by the exponential function N(t) = 240(0.85)^t, where t is the number of years since the study began. Interpret the meaning of the parameters 240 and 0.85 in this context.
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. Aroha's investment grows according to y = 9500(1.12)^x. What does 9500 represent? What does 1.12 represent?

…and 4 more problems