Exponential Growth Problem

[Random-Hero-]

1. The problem statement, all variables and given/known data

An investment pays 8% interest, compounded annually.

a) Write an equation that expresses the amount, A, of the investment as a function of time, t, in years.

b) Determine how long it will take for this investment to 1. Double in value, and 2. Triple in value.

c) Determine the percent increase in value of the account after 1. 5 years, and 2. 10 years.

d) Explain why the answers to parts b) and c) do not depend on the amount of the initial principle.


3. The attempt at a solution

a) A(t) = Ao(1.08)t

b) 1. t = ln 2 / ln1.08
2. t = ln 3 / ln1.08

c) I'm just going to use a random number, lets say $100.

1. 100(1.08)^5 = 146.93 -----> increase is 46.9%
2. 100(1.08)^10 = 215.89 -----> increase is 215%




So can anyone let me know how I did?

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c) I'm just going to use a random number, lets say $100.

1. 100(1.08)^5 = 146.93 -----> increase is 46.9%
2. 100(1.08)^10 = 215.89 -----> increase is 215%


1 is correct. 2 should be 215.89 -100 = 115.89 % because

215.89 = 100(1 + (115.89/100)) = 100 + (115.89% of 100)