2b:null 2c:["$","title",null,{"children":"Exponential Functions and Competing Function Model Validation | AxiomTutor | Observable"}] 31:[] 2f:{"id":"da2649f0d828aebf","slug":null,"title":"Exponential Functions and Competing Function Model Validation","thumbnail":"15130ec1da89c6913b984941d7275b0a2db9b77743529a34a1bd4e1ff4af2723","access_level":"public","create_time":"$D2023-10-08T20:29:40.403Z","update_time":"$D2023-10-08T22:04:44.597Z","view_time":null,"first_public_time":"$D2023-10-08T20:29:40.403Z","has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"09c31aeb403ca87c","login":"axiom-tutor","name":"AxiomTutor","avatar_url":"https://avatars-next.observableusercontent.com/2bf1d793dac61ef22bdbbceae725f52d3b12334d88b2ecaf61864a154e830f64","tier":"starter_2024","bio":"Mathematician focused on teaching advanced mathematics in a \"reconstuctive\" way."},"version":41,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"29f8a483928726bc","login":"axiom7","name":"Axiom","avatar_url":"https://avatars-next.observableusercontent.com/ad1f41069aec7011f5912c322e8999450aaf31252cd1d9a43f1ed7551f2c4ea1","tier":null,"bio":""}],"members":[{"type":"individual","id":"29f8a483928726bc","login":"axiom7","name":"Axiom","avatar_url":"https://avatars-next.observableusercontent.com/ad1f41069aec7011f5912c322e8999450aaf31252cd1d9a43f1ed7551f2c4ea1","tier":null,"role":"editor"},{"type":"team","id":"09c31aeb403ca87c","login":"axiom-tutor","name":"AxiomTutor","avatar_url":"https://avatars-next.observableusercontent.com/2bf1d793dac61ef22bdbbceae725f52d3b12334d88b2ecaf61864a154e830f64","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":0,"collection":{"id":"13a60a15c7c6e051","slug":"exercise-sets","title":"Exercise sets","owner":{"id":"09c31aeb403ca87c","login":"axiom-tutor","name":"AxiomTutor"}},"type":"notebook","body":{"titling":"auto","title":"Exponential Functions and Competing Function Model Validation","cells":[{"id":0,"value":"# Exponential Functions and Competing Function Model Validation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":5,"value":"## Exponential Functions\n\n### Exercise 1\n\nSuppose that ${tex`f`} is an exponential function and ${tex`f(1)=1`} and ${tex`f(2)=2`}. Find ${tex`f`}.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":9,"value":"### Exercise 2\n\nThe mass of a radioactive chemical decays as an exponential function, and its half-life is two years. If the initial quantity of chemical is 100 kilograms, find the exponential model of the mass.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":11,"value":"### Exercise 3\n\nSuppose that $100 is in a bank account, and after the first year, it accrues 3% interest. \n\n(a) What does the following expression represent?\n\n${tex.block`100(1+0.03)`}\n\n(b) What does ${tex`100(1+0.03)^2`} represent?\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":16,"value":"## Competing Function Model Validation\n\n### Exercise 1\n\n(a) Find the residual plot of the data \n\n${html`\n\n\n\n\n \n \n \n \n\n\n \n \n \n \n\n`}\n\nwith the model ${tex`f(x) = x^3-x`}.\n\n(b) Does the model over-estimate or under-estimate the true value which corresponds to ${tex`x=1, x=2, x=3`}?","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":33,"value":"### Exercise 2\n\nFor the data set, ${tex.block`f(1)=2\\\\f(2)=4\\\\f(3)=7`}\n\ncompare an exponential versus a linear model.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"}],"files":"$W31","stdlib":"1"}} 30:"$2f:body"

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