The investment P = $2500, interest  rate .

Formula for continuous compounding : .

Substitute the values : P = $2500 and r = 0.045.

.

(a)

The time required for the amount to double, means that, A = P + P = $5000.

Substitute the value A = $5000 in

             (Divide each side by 2500)

                           (Take natural log of each side)

                             (Apply inverse property: )

                                (Divide each side by 0.045)

(b)

The time required for the amount to triple, means that, A = P + P + P = $7500.

Substitute the value A = $7500 in .

             (Divide each side by 2500)

                           (Take natural log of each side)

                             (Apply inverse property: )

                                (Divide each side by 0.045)

(a) The time required for the amount to double is 15.4.

(b) The time required for the amount to triple is 24.4.