Exponential Growth Worksheets Grade 9

1. 2^(x+3) - 2^(x+1) = 96
2. A scientist is studying a population of algae in a pond. The algae population grows according to the function P(t) = 1200 × 2^(t/4), where P(t) is the population after t days. How many algae will be in the pond after 12 days?
3. Liam is studying bacterial growth in his biology class. He starts with a colony of 500 bacteria that doubles every 3 hours. Using the exponential growth formula A = P(2)^(t/h), where A is the final amount, P is the initial population, t is time in hours, and h is the doubling time, how many bacteria will there be after 15 hours?

…and 5 more problems

1. Noah is studying two different growth models for a science fair project. The exponential function f(x) = 6^x models the spread of a population of bacteria, while the quadratic function g(x) = x^6 models the growth of a plant's height in centimeters. For large values of x, which function grows faster and why? Show by evaluating both functions at x = 6 and x = 11, and explain how the comparison demonstrates that exponential growth eventually exceeds polynomial growth.
2. On a coordinate plane, Liam graphs two functions: y = 3^x and y = x^3. For x = 9, which function has the greater value? Then, consider the graphs for very large x values (like x = 15). Which function will eventually dominate and grow faster?
3. Charlotte is comparing two investment options for a school project. Option A grows linearly: its value after x years is given by f(x) = 12x + 100. Option B grows exponentially: its value after x years is given by g(x) = 2^x. She wants to determine after how many complete years the exponential investment will first exceed the linear investment. At what year does this happen?

…and 4 more problems

1. A research scientist is studying the spread of a new virus in a city with a population of 50,000 people. The number of infected people follows an exponential growth model I(t) = 200 × e^(0.15t), where t is time in weeks since tracking began. How many people will be infected after 4 weeks? Round your answer to the nearest whole number.
2. A right triangle is drawn on a coordinate plane with vertices at (0,0), (6,0), and (6,8). A circle is circumscribed around the triangle such that all three vertices lie on the circle's circumference. What is the area of this circumscribed circle? (Use π = 3.14)
3. Tane is studying the growth of two functions to demonstrate a key mathematical principle. He defines an exponential function f(x) = 11^x and a cubic function g(x) = x^9. For large positive integer values of x, which function will eventually produce larger outputs? Evaluate both functions at x = 12 and x = 18, and use these comparisons to explain why exponential growth eventually exceeds polynomial growth.

…and 4 more problems