Exponential Form Worksheets Grade 9

1. Aroha is analyzing a population of rare ferns in a conservation area. The graph below (described in words) shows the number of ferns over time. At time t = 0 (the year 2020), there are 27 ferns. The population triples every 3 years. The graph passes through the points (0, 27), (3, 81), and (6, 243). Write an exponential function of the form f(t) = a * b^t that models the number of ferns after t years.
2. Isabella is tracking the spread of a rumor in her school. She creates a graph where the x-axis represents time in hours (t) and the y-axis represents the number of students who have heard the rumor. The graph passes through the points (0, 12) and (3, 324). If the rumor spreads according to an exponential function of the form f(t) = a · b^t, what is the value of b (the growth factor per hour)?
3. A pharmaceutical company is testing a new medication that decays exponentially in the bloodstream. A patient takes a 400 mg dose, and after 6 hours, only 50 mg remains active. Write an exponential function in the form M(t) = ab^t that models the amount of active medication in milligrams after t hours.

…and 4 more problems

1. 2^(3x+1) = 128 = ?
2. A population starts at 200 and doubles every 4 years. Write the exponential function in the form f(t) = a·b^t where t is measured in years.
3. A city's population is currently 80,000 people and is growing at a rate of 5% per year. Write an exponential function in the form P(t) = ab^t that models the population after t years.

…and 6 more problems

1. Olivia is studying a population of bacteria in a petri dish. At time t = 0 hours, she observes that there are 40 bacteria. The population grows exponentially, and after 3 hours, the number of bacteria has increased to 320. Write an exponential function of the form f(t) = a * b^t that models the number of bacteria after t hours.
2. Lena is studying the spread of a social media post. When she first shares it, 15 people see it immediately. The number of people who see the post triples every 2 hours. Write an exponential function in the form V(t) = a * b^t that models the number of viewers V after t hours.
3. Isabella is studying the growth of a bacterial colony on a petri dish. She observes that the colony starts as a small circle with area 27 square millimeters. Every 2 hours, the area of the colony triples. Write an exponential function of the form f(t) = a · b^t that models the area of the colony (in square millimeters) after t hours.

…and 5 more problems