Difference between revisions of "Math 22 Exponential Growth and Decay"
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is proportional to the quantity present at any time <math>t</math>, then is of the form | is proportional to the quantity present at any time <math>t</math>, then is of the form | ||
<math>y=Ce^{kt}</math> | <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>. | + | 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 (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}
is a positive quantity whose rate of change with respect to time
is proportional to the quantity present at any time 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 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