SOLUTION: For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, , let r = 8%, P = 1, and n = 1 and give

Algebra ->  Graphs -> SOLUTION: For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, , let r = 8%, P = 1, and n = 1 and give      Log On


   

Question 86388: For a fixed rate, a fixed principal amount, and a fixed compounding cycle, the return is an exponential function of time. Using the formula, , let r = 8%, P = 1, and n = 1 and give the coordinates (t,A) for the points where t = 0, 1, 2, 3, 4. Round your answer to the hundredth's place.

a) Show coordinates in this space.

Show work in this space.


b) Show graph here.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)
A=p%281%2Br%2Fn%29%5E%28n%2At%29 Start with the given equation

A=1%281%2B0.08%2F1%29%5E%281%2At%29 Plug in p=1, r=0.08, and n=1
Let t=0 and plug it into A=1%281%2B0.08%2F1%29%5E%281%2At%29
A=1%281%2B0.08%2F1%29%5E%281%2A0%29 Start with the given expression
A=1%281%2B0.08%29%5E%281%2A0%29 Divide 0.08 by 1 to get 0.08
A=1%281%2B0.08%29%5E%280%29 Multiply the exponents 1 and 0 to get 0
A=1%281.08%29%5E%280%29 Add 1 and 0.08 to get 1.08
A=1%281%29 Raise 1.08 to 0 to get 1
A=1 Multiply 1 and 1 to get 1
So our 1st point is (0,1)

Let t=1 and plug it into A=1%281%2B0.08%2F1%29%5E%281%2At%29
A=1%281%2B0.08%2F1%29%5E%281%2A1%29 Start with the given expression
A=1%281%2B0.08%29%5E%281%2A1%29 Divide 0.08 by 1 to get 0.08
A=1%281%2B0.08%29%5E%281%29 Multiply the exponents 1 and 1 to get 1
A=1%281.08%29%5E%281%29 Add 1 and 0.08 to get 1.08
A=1%281.08%29 Raise 1.08 to 1 to get 1.08
A=1.08 Multiply 1 and 1.08 to get 1.08
So our 2nd point is (1,1.08)

Let t=2 and plug it into A=1%281%2B0.08%2F1%29%5E%281%2At%29
A=1%281%2B0.08%2F1%29%5E%281%2A2%29 Start with the given expression
A=1%281%2B0.08%29%5E%281%2A2%29 Divide 0.08 by 1 to get 0.08
A=1%281%2B0.08%29%5E%282%29 Multiply the exponents 1 and 2 to get 2
A=1%281.08%29%5E%282%29 Add 1 and 0.08 to get 1.08
A=1%281.1664%29 Raise 1.08 to 2 to get 1.1664
A=1.1664 Multiply 1 and 1.1664 to get 1.1664
So our 3rd point is (2,1.1664)

Let t=3 and plug it into A=1%281%2B0.08%2F1%29%5E%281%2At%29
A=1%281%2B0.08%2F1%29%5E%281%2A3%29 Start with the given expression
A=1%281%2B0.08%29%5E%281%2A3%29 Divide 0.08 by 1 to get 0.08
A=1%281%2B0.08%29%5E%283%29 Multiply the exponents 1 and 3 to get 3
A=1%281.08%29%5E%283%29 Add 1 and 0.08 to get 1.08
A=1%281.259712%29 Raise 1.08 to 3 to get 1.259712
A=1.259712 Multiply 1 and 1.259712 to get 1.259712
So our 4th point is (3,1.259712)

Let t=4 and plug it into A=1%281%2B0.08%2F1%29%5E%281%2At%29
A=1%281%2B0.08%2F1%29%5E%281%2A4%29 Start with the given expression
A=1%281%2B0.08%29%5E%281%2A4%29 Divide 0.08 by 1 to get 0.08
A=1%281%2B0.08%29%5E%284%29 Multiply the exponents 1 and 4 to get 4
A=1%281.08%29%5E%284%29 Add 1 and 0.08 to get 1.08
A=1%281.36048896%29 Raise 1.08 to 4 to get 1.36048896
A=1.36048896 Multiply 1 and 1.36048896 to get 1.36048896
So our 5th point is (4,1.36048896)

b)

Here is a table of all of our points: 



 xy




 01
 

 11.08
 

 21.1664
 

 31.259712
 

 41.36048896

So lets graph these points and connect them