if a(t) is the amount of the investment at time t for the case of continuous compounding, write a differential equation satisfied by a(t). Let the rate be r. Then the amount of the investment must satisfy the differential equation A′ (t) = r A (t)
The initial condition satisfied by A (t) is its value at t = 0. At t=0, no compounding has occurred yet, and the amount is equal to the original amount invested, called the principal. If the principal is P, then the initial condition is A (0) = P

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smecloudbird18 smecloudbird18 · Answer 1 · 2022-11-30T07:14:34+01:00

The differential equation that satisfies the given amount of investment is A'(t) = rA(t)

Let the rate of investment = r

The amount of investment must satisfy the differential equation

A'(t) = r A(t)

Initial condition is the value of A(t) at t = 0

No compounding will be applied at t = 0 and the amount is equal to the original amount invested, known as principal.

If the Principal amount is P, then the initial condition is A(0) = P

Hence, the differential equation is A'(t) = rA(t)

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