SOLUTION: Please help me solve this: For a fixed rate, a fixed principal amount and a fixed compounding cycle, the return is an exponential function of time. Using a formula, let r = 10%,

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Question 83425: Please help me solve this:
For a fixed rate, a fixed principal amount and a fixed compounding cycle, the return is an exponential function of time. Using a formula, let r = 10%, 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 nearest tenth's place.
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
A=p%281%2Br%2Fn%29%5E%28n%2At%29 Start with the given equation

A=1%281%2B0.1%2F1%29%5E%281%2At%29 Plug in p=1, r=0.1, and n=1
Let t=0 and plug it into A=1%281%2B0.1%2F1%29%5E%281%2At%29
A=1%281%2B0.1%2F1%29%5E%281%2A0%29 Start with the given expression
A=1%281%2B0.1%29%5E%281%2A0%29 Divide 0.1 by 1 to get 0.1
A=1%281%2B0.1%29%5E%280%29 Multiply the exponents 1 and 0 to get 0
A=1%281.1%29%5E%280%29 Add 1 and 0.1 to get 1.1
A=1%281%29 Raise 1.1 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%2B0.1%2F1%29%5E%281%2At%29
A=1%281%2B0.1%2F1%29%5E%281%2A1%29 Start with the given expression
A=1%281%2B0.1%29%5E%281%2A1%29 Divide 0.1 by 1 to get 0.1
A=1%281%2B0.1%29%5E%281%29 Multiply the exponents 1 and 1 to get 1
A=1%281.1%29%5E%281%29 Add 1 and 0.1 to get 1.1
A=1%281.1%29 Raise 1.1 to 1 to get 1.1
A=1.1 Multiply 1 and 1.1 to get 1.1
So our 2nd point is (1,1.1)

Let t=2 and plug it into A=1%281%2B0.1%2F1%29%5E%281%2At%29
A=1%281%2B0.1%2F1%29%5E%281%2A2%29 Start with the given expression
A=1%281%2B0.1%29%5E%281%2A2%29 Divide 0.1 by 1 to get 0.1
A=1%281%2B0.1%29%5E%282%29 Multiply the exponents 1 and 2 to get 2
A=1%281.1%29%5E%282%29 Add 1 and 0.1 to get 1.1
A=1%281.21%29 Raise 1.1 to 2 to get 1.21
A=1.21 Multiply 1 and 1.21 to get 1.21
So our 3rd point is (2,1.21)

Let t=3 and plug it into A=1%281%2B0.1%2F1%29%5E%281%2At%29
A=1%281%2B0.1%2F1%29%5E%281%2A3%29 Start with the given expression
A=1%281%2B0.1%29%5E%281%2A3%29 Divide 0.1 by 1 to get 0.1
A=1%281%2B0.1%29%5E%283%29 Multiply the exponents 1 and 3 to get 3
A=1%281.1%29%5E%283%29 Add 1 and 0.1 to get 1.1
A=1%281.331%29 Raise 1.1 to 3 to get 1.331
A=1.331 Multiply 1 and 1.331 to get 1.331
So our 4th point is (3,1.331)

Let t=4 and plug it into A=1%281%2B0.1%2F1%29%5E%281%2At%29
A=1%281%2B0.1%2F1%29%5E%281%2A4%29 Start with the given expression
A=1%281%2B0.1%29%5E%281%2A4%29 Divide 0.1 by 1 to get 0.1
A=1%281%2B0.1%29%5E%284%29 Multiply the exponents 1 and 4 to get 4
A=1%281.1%29%5E%284%29 Add 1 and 0.1 to get 1.1
A=1%281.4641%29 Raise 1.1 to 4 to get 1.4641
A=1.4641 Multiply 1 and 1.4641 to get 1.4641
So our 5th point is (4,1.4641)
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%2B0.1%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%2C1.1%2C0.08%29%2C%0D%0Acircle%281%2C1.1%2C0.05%29%2C%0D%0Acircle%282%2C1.21%2C0.08%29%2C%0D%0Acircle%282%2C1.21%2C0.05%29%2C%0D%0Acircle%283%2C1.331%2C0.08%29%2C%0D%0Acircle%283%2C1.331%2C0.05%29%2C%0D%0Acircle%284%2C1.4641%2C0.08%29%2C%0D%0Acircle%284%2C1.4641%2C0.05%29%0D%0A%29

Answer by stanbon(48535) About Me  (Show Source):
You can put this solution on YOUR website!
For a fixed rate, a fixed principal amount and a fixed compounding cycle, the return is an exponential function of time. Using a formula, let r = 10%, 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 nearest tenth's place.
----------------
A(t) = P(1+r/n)^(nt)
(0,1)
(1,1.1)
(2,1.0192)
(3,1.029)
(4,1.0389)
===============
Cheers,
Stan H.