https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-vs-linear-growth/v/exponential-growth-functions 2022-11-16T04:22:43.7414897Z Intro to exponential functions An exponential function represents the relationship between an input and output, where we use repeated multiplication on an initial value to get the output for any given input. Exponential functions can grow or decay very quickly. Exponential functions are often used to model things in the real world, such as populations, radioactive materials, and compound interest. Sal Khan video https://cdn.kastatic.org/googleusercontent/MOdCeqFGlDqk69XEhUqpMPoJA42wLRt7GwZjEAthvS_AxHPH0ieVuA4DqeI3ImMs5u7K5aCZdV6MCqKxXrs-d4g Intro to exponential functions An exponential function represents the relationship between an input and output, where we use repeated multiplication on an initial value to get the output for any given input. Exponential functions can grow or decay very quickly. Exponential functions are often used to model things in the real world, such as populations, radioactive materials, and compound interest. https://cdn.kastatic.org/ka-youtube-converted/6WMZ7J0wwMI.mp4/6WMZ7J0wwMI.mp4 461 Exponential growth and decay https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:graphs-of-exponential-growth/v/graphing-exponential-functions 2023-05-24T15:30:27.32390848Z Exponential function graph We can graph an exponential function, like y=5ˣ, by picking a few inputs (x-values) and finding their corresponding outputs (y-values). We'll see that an exponential function has a horizontal asymptote in one direction and rapidly changes in the other direction. Sal Khan video https://cdn.kastatic.org/googleusercontent/ntaWYGvlJPukwyhP7oC72DTO8x4xLVpcF5KAFo38Bh93MyaHdExf2ElxhokBqnWf3H-UmjGETTe2s0_Kv9rod86J1A Exponential function graph We can graph an exponential function, like y=5ˣ, by picking a few inputs (x-values) and finding their corresponding outputs (y-values). We'll see that an exponential function has a horizontal asymptote in one direction and rapidly changes in the other direction. https://cdn.kastatic.org/ka-youtube-converted/9SOSfRNCQZQ.mp4/9SOSfRNCQZQ.mp4 332 Exponential growth and decay https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:graphs-of-exponential-growth/v/graphs-of-exponential-growth 2021-02-16T05:02:26Z Graphs of exponential growth Identifying which graph represents a given exponential function. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Graphs of exponential growth Identifying which graph represents a given exponential function. https://cdn.kastatic.org/ka-youtube-converted/6rX2VNybXEE.mp4/6rX2VNybXEE.mp4 261 Exponential growth and decay https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:graphs-of-exponential-growth/e/graphing-exponential-growth-intro 2025-03-03T19:47:54.930712342Z Graphs of exponential growth Start exploring the relationship between exponential functions and their graphs. Tomer Gal exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-decay/v/exponential-decay-intro 2022-11-16T04:22:43.7414897Z Exponential decay intro Both exponential growth and decay functions involve repeated multiplication by a constant factor. However, the difference lies in the size of that factor: - In an exponential growth function, the factor is greater than 1, so the output will increase (or "grow") over time. - In an exponential decay function, the factor is between 0 and 1, so the output will decrease (or "decay") over time. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Exponential decay intro Both exponential growth and decay functions involve repeated multiplication by a constant factor. However, the difference lies in the size of that factor: - In an exponential growth function, the factor is greater than 1, so the output will increase (or "grow") over time. - In an exponential decay function, the factor is between 0 and 1, so the output will decrease (or "decay") over time. https://cdn.kastatic.org/ka-youtube-converted/v4IdaXvyE7U.mp4/v4IdaXvyE7U.mp4 492 Exponential growth and decay https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-decay/e/exponential-growth-vs-decay 2025-03-07T16:29:07.940270514Z Exponential growth vs. decay Identify whether an exponential functions represents growth or decay. Tomer Gal exercise