Exponential Parameters Worksheets Grade 11

1. A biologist is studying bacterial growth in a lab culture. The initial population is 500 bacteria, and it doubles every 3 hours. The growth can be modeled by the function P(t) = P₀ * e^(kt), where t is time in hours. Determine the value of the continuous growth rate constant k, and then calculate the population after 9 hours.
2. Isabella's investment grows according to I(t) = 1200(1.072)^t, where t is years. What does 1200 represent? What does 1.072 represent?
3. Sophia's investment grows according to V(t) = 1600(1.06)^t, where t is time in years. What does the number 1600 represent? What does the number 1.06 represent?

…and 5 more problems

1. Aroha's investment grows according to V(t) = 950(1.12)^t, where V is the value in dollars and t is time in years. What does the number 950 represent? What does the number 1.12 represent?
2. Matiu is studying the depreciation of a specialized piece of forestry equipment. He models its value using the exponential function V(t) = 48000 × (0.78)^t, where V(t) is the value in dollars after t years. Interpret the meaning of the parameters 48000 and 0.78 in the context of the equipment's value over time.
3. A research team is studying bacterial growth in a lab culture. The initial population is 500 bacteria, and it doubles every 3 hours. The growth can be modeled by the function P(t) = P₀ * e^(kt), where t is time in hours. Determine the value of the continuous growth rate constant k, and then calculate the population after 9 hours.

…and 4 more problems

1. Kaia is studying the growth of a fern species in a forest regeneration project. The height of the fern is modeled by the exponential function H(t) = 7 × (1.21)^t, where H(t) is the height in centimeters after t months. Interpret the meaning of the parameters 7 and 1.21 in this context.
2. Sophia is studying a bacterial culture that grows according to the function P(t) = 750(1.12)^t, where t is time in hours. What does the number 750 represent in this context? What does the number 1.12 represent?
3. Aroha's investment grows according to V(t) = 375(1.15)^t, where t is in years. What does 375 represent? What does 1.15 represent?

…and 5 more problems