Exponential Growth Worksheets Grade 9

1. Compare f(x)=10^x and g(x)=x^10 for x=11
2. A research team is studying the spread of a new social media trend. On day 1, 50 people shared the trend. The number of people sharing grows exponentially, tripling every 2 days. Using the exponential growth model N(t) = N₀ × a^t, where N₀ is the initial number, t is time in days, and a is the daily growth factor, determine how many people will be sharing the trend after 8 days.
3. 2^3 × 3^2 - √81 = ?

…and 4 more problems

1. A research lab is studying bacterial growth in a petri dish. The initial population is 200 bacteria, and the population doubles every 3 hours. Write an exponential function in the form P(t) = P₀ * a^t that models the bacterial population after t hours, where P₀ is the initial population and a is the growth factor per hour.
2. Hana is comparing the growth of two functions on a coordinate plane: the exponential function f(x) = 12^x and the polynomial function g(x) = x^12. She graphs both for x ≥ 1 and observes that the polynomial function is larger for some small values of x. Determine the smallest integer value of x greater than 1 for which f(x) = 12^x first exceeds g(x) = x^12.
3. A rare orchid species in a botanical garden is growing exponentially. The number of orchids is modeled by the function O(t) = 120 × 2^(t/4), where t is the time in months. How many orchids will there be after 12 months?

…and 5 more problems

1. A research scientist named Maya is studying the spread of a new virus in a city with a population of 50,000 people. The virus spreads such that the number of infected people triples every 5 days. If there are initially 20 infected people, write an exponential function in the form I(t) = I₀ × b^t that models the number of infected people after t days, where I₀ is the initial number and b is the daily growth factor. Then, determine the daily growth factor b.
2. Tane is analyzing two functions on a coordinate plane: the exponential function f(x) = 2^x and the quadratic function g(x) = x^2. He notices that for small values of x, the quadratic appears to be above the exponential. However, he wants to determine the exact integer x-values greater than 8 where the exponential function's output first becomes greater than the quadratic's output, and then continues to stay greater for all larger x. Find the smallest integer x greater than 8 such that 2^x > x^2, and confirm that this inequality holds for the next two consecutive integer x-values as well.
3. Mason is comparing two functions on a coordinate plane. The first function is f(x) = 9^x, and the second function is g(x) = x^9. He plots both graphs for x ≥ 0. For what smallest integer value of x does the graph of f(x) first exceed the graph of g(x)?

…and 4 more problems