SOLUTION: 4) 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

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: 4) 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      Log On

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Question 86387: 4) 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.
b) Most calculators have 2 different logs on them: log, which is base 10, and ln, which is base e. In computer science, digital computers are based on the binary numbering system which means that there are only 2 numbers available to the computer, 0 and 1. When a computer scientist needs a logarithm, he needs a log to base 2 which is not on any calculator. To find the log of a number to any base, we can use a conversion formula as shown here:

Using this formula, find . Round your answer to the hundredth's place.
Answer:
Show work in this space.

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
4)
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

drawing%28500%2C500%2C-5%2C5%2C-5%2C5%2C%0D%0Agraph%28+500%2C+500%2C+-5%2C+5%2C+-5%2C+5%2C1%281%2B0.08%2F1%29%5E%281%2Ax%29%29%2C%0D%0Agrid%281%29%2C%0D%0Acircle%280%2C1%2C0.08%29%2C%0D%0Acircle%280%2C1%2C0.05%29%2C%0D%0Acircle%281%2C1.08%2C0.08%29%2C%0D%0Acircle%281%2C1.08%2C0.05%29%2C%0D%0Acircle%282%2C1.1664%2C0.08%29%2C%0D%0Acircle%282%2C1.1664%2C0.05%29%2C%0D%0Acircle%283%2C1.259712%2C0.08%29%2C%0D%0Acircle%283%2C1.259712%2C0.05%29%2C%0D%0Acircle%284%2C1.36048896%2C0.08%29%2C%0D%0Acircle%284%2C1.36048896%2C0.05%29%0D%0A%29

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The problem doesn't show up, all it says is:

"Using this formula, find ."

where I'm assuming the problem would be