https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-functions-from-tables-graphs/v/writing-exponential-functions 2022-10-06T23:01:00.745424633Z Writing exponential functions Writing the exponential function whose initial value is -2 and common ratio is 1/7. video https://cdn.kastatic.org/ka_thumbnails_cache/33469136-0c70-49f7-8a6f-d3e0096f6a69_1280_720_base.png Writing exponential functions Writing the exponential function whose initial value is -2 and common ratio is 1/7. https://cdn.kastatic.org/ka-youtube-converted/UgLfAb_aFt4.mp4/UgLfAb_aFt4.mp4 100 Funciones exponenciales a partir de tablas y gráficos https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-functions-from-tables-graphs/v/constructing-linear-and-exponential-functions-from-data 2022-11-16T04:22:43.7414897Z Writing exponential functions from tables Both linear equations and exponential equations represent relationships between two variables. However, the way that the variables are related to each other in each type of equation is different. A linear equation can be thought of as representing repeated addition on an initial value, while an exponential equation can be thought of as representing repeated multiplication on an initial value. Sal Khan video https://cdn.kastatic.org/googleusercontent/C5E0AHbbT000Om4TzshxvNdTtKSUxFTwSCv7279hr2f9nAuBIn1FlMtEYNqfDXNNM6OXVZhU8J-mnEt38Cc63dInoQ Writing exponential functions from tables Both linear equations and exponential equations represent relationships between two variables. However, the way that the variables are related to each other in each type of equation is different. A linear equation can be thought of as representing repeated addition on an initial value, while an exponential equation can be thought of as representing repeated multiplication on an initial value. https://cdn.kastatic.org/ka-youtube-converted/Qst1UVtq8pE.mp4/Qst1UVtq8pE.mp4 317 Funciones exponenciales a partir de tablas y gráficos https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-functions-from-tables-graphs/e/construct-basic-exponential-functions-from-table-or-graph 2023-12-12T00:32:03.629852833Z Exponential functions from tables & graphs Write exponential functions of the basic form f(x)=a⋅rˣ, either when given a table with two input-output pairs, or when given the graph of the function. Sid Patel exercise https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-functions-from-tables-graphs/v/constructing-linear-and-exponential-functions-from-graph 2022-11-16T04:22:43.7414897Z Writing exponential functions from graphs Given a graph of a line, we can write a linear function in the form y=mx+b by identifying the slope (m) and y-intercept (b) in the graph. GIven a graph of an exponential curve, we can write an exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph. Sal Khan video https://cdn.kastatic.org/googleusercontent/62pxi7wErqGyMz2IbFpUuy_2BykQgj3aKuxDUDicMECiIfndQ_Ky8fd9heJ0Y4-2mNSWQVN8d4-62IpP3aDvZ1ub Writing exponential functions from graphs Given a graph of a line, we can write a linear function in the form y=mx+b by identifying the slope (m) and y-intercept (b) in the graph. GIven a graph of an exponential curve, we can write an exponential function in the form y=ab^x by identifying the common ratio (b) and y-intercept (a) in the graph. https://cdn.kastatic.org/ka-youtube-converted/gFdh_rE2XgU.mp4/gFdh_rE2XgU.mp4 445 Funciones exponenciales a partir de tablas y gráficos https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-functions-from-tables-graphs/v/analyzing-tables-of-exponential-functions 2022-11-16T04:22:43.7414897Z Analyzing tables of exponential functions Here is how we can write an equation for an exponential function from a table of values: 1. Determine the common ratio. For example, if we see that every time x increases by 1, y is multiplied by 2, then the common ratio is 2. 2. Find the initial value of the function, or the y-intercept. This is the y-value when x=0. 3. Write the equation in the form y = ab^x, where a is the initial value and b is the common ratio. video https://cdn.kastatic.org/ka_thumbnails_cache/e763c042-ad9e-4e5f-9181-d16b0e6d681a_1280_720_base.png Analyzing tables of exponential functions Here is how we can write an equation for an exponential function from a table of values: 1. Determine the common ratio. For example, if we see that every time x increases by 1, y is multiplied by 2, then the common ratio is 2. 2. Find the initial value of the function, or the y-intercept. This is the y-value when x=0. 3. Write the equation in the form y = ab^x, where a is the initial value and b is the common ratio. https://cdn.kastatic.org/ka-youtube-converted/yOqhKOicqhU.mp4/yOqhKOicqhU.mp4 440 Funciones exponenciales a partir de tablas y gráficos https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-functions-from-tables-graphs/v/analyzing-graph-of-exponential-function 2021-02-16T05:02:26Z Analyzing graphs of exponential functions Given the graph of an exponential function, Sal finds the formula of the function and a value that is outside the graph. video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw Analyzing graphs of exponential functions Given the graph of an exponential function, Sal finds the formula of the function and a value that is outside the graph. https://cdn.kastatic.org/ka-youtube-converted/fe1Hsqyetzk.mp4/fe1Hsqyetzk.mp4 246 Funciones exponenciales a partir de tablas y gráficos https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-functions-from-tables-graphs/v/analyzing-exponential-graph-with-negative-initial-value 2022-10-06T23:01:00.745424633Z Analyzing graphs of exponential functions: negative initial value Given the graph of an exponential function with a negative initial value, Sal finds the formula of the function and solves an equation. video https://cdn.kastatic.org/ka_thumbnails_cache/c3c33387-a042-4c10-8143-7c8fcce8fac3_1280_720_base.png Analyzing graphs of exponential functions: negative initial value Given the graph of an exponential function with a negative initial value, Sal finds the formula of the function and solves an equation. https://cdn.kastatic.org/ka-youtube-converted/No1LKevjF6U.mp4/No1LKevjF6U.mp4 367 Funciones exponenciales a partir de tablas y gráficos https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-functions-from-tables-graphs/v/modeling-ticket-fines-with-exponential-function 2021-02-16T05:02:27Z Modeling with basic exponential functions word problem Sal solves a word problem where he models the growth of a speeding ticket fine over time as an exponential function, and then interprets this model. Sal Khan video https://cdn.kastatic.org/googleusercontent/wuRw89gHQGCwT8wUU8CyPaY7_MynKjgiZ28KDPk7UiI-htiYMcwRAGXRQszDZt_su3I4gRwTyMuH6PVdQMlLRlMF Modeling with basic exponential functions word problem Sal solves a word problem where he models the growth of a speeding ticket fine over time as an exponential function, and then interprets this model. https://cdn.kastatic.org/ka-youtube-converted/2iZXFd_ZImA.mp4/2iZXFd_ZImA.mp4 337 Funciones exponenciales a partir de tablas y gráficos https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:exponential-growth-decay/x2f8bb11595b61c86:exponential-functions-from-tables-graphs/e/exponential-graph-context 2026-03-13T13:00:37.125063205Z Connecting exponential graphs with contexts Practice connecting a context involving exponential growth or decay with its graph. Jeff Dodds exercise