# exponential function

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 double in value and then to triple in value.

c) determine the percent increase in value of the account after 5 years and then after 10 years.

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

Can someone explain to me how to get started? I do not know where to start except for the fact that I need to make an exponential function.

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1. after one year
A = Ao (1.08)
after two years
A = Ao (1.08)(1.08)
after three years
A = Ao (1.08)(1.08)(1.08)
after t years
A = Ao (1.08)^t

When is A/Ao = 2?
2 = 1.08^t
log 2 = t log 1.08
.301 = t * .0334
t = 9.01 years to double

That should get you started.

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2. did i do part c right?

c) determine the percent increase in value of the account after:
5 years,
A=(1.08)^5
=1.47
therefore 1.47 % increase???

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3. c) continued:
after 10 years
A=(1.08)^10
=2.16
therefore 2.16% increase?

Am I doing this right?

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

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4. " =1.47
therefore 1.47 % increase??? "

A factor of 1.47 is a 47% increase
100 * final/original = 147/1 =147 %
which is 47 % over the original 100%

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5. 2.16 * 100 = 216 % of original
216 % - original 100% = 116% increase

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