Question

The value P(t), in dollars, of bank account is growing according to the equation. dP/dt - 0.05P = 15. If an initial amount of P(0) = $1,300 is deposited to the account, then the future value of this account at time t = 6 is approximately

Answer 1

The given differential equation is dP/dt - 0.05P = 15. Solving this first-order linear differential equation, we get P(t) = Ce^(0.05t) + 300, where C is a constant of integration. Since P(0) = 1300, we have C = 1300 - 300 = 1000. Therefore, the solution to the differential equation is P(t) = 1000e^(0.05t) + 300.

Substituting t = 6 into this expression for P(t), we find that the future value of the account at time t = 6 is approximately P(6) = 1000e^(0.05 * 6) + 300 ≈ $1,349.86.

So the future value of this account at time t = 6 is approximately $1,349.86.