A quantity P(t) representing the value of an investment is known to grow continuously at a rate proportional to its current value. Answer the following questions.
a. Part 1: (i) Show that the general solution of the differential equation dtdP=kP can be written in the form P(t)=P0ekt, where P0=P(0).
b. Part 2: (ii) An amount of ₹50000 grows to ₹80000 in 5 years under such continuous growth. Determine the annual growth constant k correct to two decimal places.
c. Part 3: (iii) Using the value of k obtained in part (ii), calculate the value of the investment after a total period of 9 years from the initial deposit.