Difference between revisions of "Math 22 Natural Exponential Functions"

From Math Wiki
Jump to navigation Jump to search
Line 7: Line 7:
 
   Let <math>P</math> be the amount deposited, <math>t</math> the number of years, <math>A</math> the balance,  
 
   Let <math>P</math> be the amount deposited, <math>t</math> the number of years, <math>A</math> the balance,  
 
   and <math>r</math> the annual interest rate (in decimal form).
 
   and <math>r</math> the annual interest rate (in decimal form).
−
   1. Compounded <math>n</math> times per year: <math>A=P(1+\frac{r}{n})^{rt}</math>
+
   1. Compounded <math>n</math> times per year: <math>A=P(1+\frac{r}{n})^{nt}</math>
 
   2. Compounded continuously: <math>A=Pe^{rt}</math>
 
   2. Compounded continuously: <math>A=Pe^{rt}</math>
  
Line 16: Line 16:
 
!Solution: &nbsp;
 
!Solution: &nbsp;
 
|-
 
|-
−
|<math>(8^{\frac{1}{2}})(2^{\frac{1}{2}})=(8\cdot 2)^{\frac{1}{2}}=16^{\frac{1}{2}}</math>
+
|<math>A=3000(1+\frac{0.04}{4})^{(4)10}</math>
 
|}
 
|}
  
−
'''a)''' Quarterly
+
'''a)''' Annually
 
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
 
{| class = "mw-collapsible mw-collapsed" style = "text-align:left;"
 
!Solution: &nbsp;
 
!Solution: &nbsp;
 
|-
 
|-
−
|<math>(8^{\frac{1}{2}})(2^{\frac{1}{2}})=(8\cdot 2)^{\frac{1}{2}}=16^{\frac{1}{2}}</math>
+
|<math>A=3000(1+\frac{0.04}{1})^{(1)10}</math>
 
|}
 
|}
  
Line 30: Line 30:
 
!Solution: &nbsp;
 
!Solution: &nbsp;
 
|-
 
|-
−
|<math>(8^{\frac{1}{2}})(2^{\frac{1}{2}})=(8\cdot 2)^{\frac{1}{2}}=16^{\frac{1}{2}}</math>
+
|<math>A=3000(1+\frac{0.04}{12})^{(12)10}</math>
 
|}
 
|}
  
Line 37: Line 37:
 
!Solution: &nbsp;
 
!Solution: &nbsp;
 
|-
 
|-
−
|<math>(8^{\frac{1}{2}})(2^{\frac{1}{2}})=(8\cdot 2)^{\frac{1}{2}}=16^{\frac{1}{2}}</math>
+
|<math>A=3000(1+\frac{0.04}{365})^{(365)10}</math>
 
|}
 
|}
  

Revision as of 07:06, 11 August 2020

Limit Definition of 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 e} 

 The irrational number 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 e}
 is defined to be the limit:
 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 \lim_{x\to 0} (1+x)^{\frac{1}{x}}=e}

 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 e\approx 2.71828182846}

Compound Interest

 Let 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 P}
 be the amount deposited, 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}
 the number of years, 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 A}
 the balance, 
 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 r}
 the annual interest rate (in decimal form).
 1. Compounded 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 n}
 times per year: 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 A=P(1+\frac{r}{n})^{nt}}

 2. Compounded continuously: 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 A=Pe^{rt}}

Exercises Find the balance in an account when $3000 is deposited for 10 years at an interest rate of 4%, compounded as follows.

a) Quarterly

Solution:  
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 A=3000(1+\frac{0.04}{4})^{(4)10}}

a) Annually

Solution:  
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 A=3000(1+\frac{0.04}{1})^{(1)10}}

a) Monthly

Solution:  
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 A=3000(1+\frac{0.04}{12})^{(12)10}}

a) Daily

Solution:  
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 A=3000(1+\frac{0.04}{365})^{(365)10}}

a) Continuously

Solution:  
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 A=Pe^{rt}=3000(e^{(0.04) (10)})}


Return to Topics Page

This page were made by Tri Phan

Retrieved from "https://wiki.math.ucr.edu/index.php?title=Math_22_Natural_Exponential_Functions&oldid=2426"