Difference between revisions of "Math 22 Exponential Growth and Decay"
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| + | ==Exponential Growth and Decay== | ||
| + | If <math>y</math> is a positive quantity whose rate of change with respect to time | ||
| + | is proportional to the quantity present at any time <math>t</math>, then is of the form | ||
| + | <math>y=Ce^{kt}</math> | ||
| + | where <math>C</math> is the initial value and <math>k</math> is the constant of proportionality. Exponential growth is indicated by <math>k>0</math> and exponential decay by <math>k<0</math>. | ||
[[Math_22| '''Return to Topics Page''']] | [[Math_22| '''Return to Topics Page''']] | ||
'''This page were made by [[Contributors|Tri Phan]]''' | '''This page were made by [[Contributors|Tri Phan]]''' | ||
Revision as of 09:11, 11 August 2020
Exponential Growth and Decay
If Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle y}
is a positive quantity whose rate of change with respect to time
is proportional to the quantity present at any time Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle t}
, then is of the form
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y=Ce^{kt}}
where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C}
is the initial value and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k}
is the constant of proportionality. Exponential growth is indicated by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k>0}
and exponential decay by Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle k<0}
.
This page were made by Tri Phan