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**Affinity** Four thousand dollars is deposited into a savings account at 3.5% interest compounded continuously.

a) What is the formula for A(t), the balance after t years?

b) What differential equation is satisfied by A(t), the balance after t years?

c) How much money will be in the account after 2 years?

d) When will the balance reach $5000?

e) How fast is the balance growing when it reaches $5000?

f) When will the balance triple?

g) How fast is the balance growing at the time it triples in value?

Thanks in advance!