Formulas!

Hello everyonee,
I hope everyone had a wonderful weekend!

A(t)=Ao(1+r)^t
-Used when compounding.
Ao=starting amount
r=rate
t= number of times compounding in given timespan.

A(t)=Aob^t/k

-Used when things are doubling, tripling, halfing, etc.

Ao=starting amount

b=doubling, tripling, etc.

t=amount of time

k=how long it takes to double, triple, half, etc.r.

Rule of 72- to find how long it takes for something to double then find 72/

r is not a decimal here

**Only used when compounding continuously

P(t)=PoE^rt

Po=starting amount

e=on ln button

r=rate

t=time

Example 1:

The half-life of a radioactive isotope is 4 days. If 3.2 kg are present now, how much will be present after:

a) 4 days

A(t)=Aob^t/k

A(t)=3.2(1/2)^(4/4)

=1.6kg

b) 8 days

A(t)=Aob^t/k

=3.2(1/2)^(8/4)

=0.8 kg

c) 20 days

A(t)= Aob^t/k

A(t)=3.2(1/2)^(20/4)

=0.1 kg

d) t days

A(t)=Aob^t/k

A(t)=3.2(1/2)^t/4

Example 2:

a)If $1000 is invested so that it grows at the rate of 10% per year, what will the investment be worth in 20 years?

A(t)=Ao(1+r)^t

A(t)=1000(1+.10)^20

=$6727

b)According to the rule of 72, in approximately how many years will the investment double in value?

72/10=7