This Question 3 pts 17 of 25 1 co Suppose that Po is investe

This Question: 3 pts 17 of 25 (1 co Suppose that Po is invested in a savings account in which interest is compounded continuously at dP-0.067P) dt (a)Find the function P() that satisfies the equation. Write it in terms of Po and 0.067 (b Suppose that $500 is invested. What is the balance after 3 years? (c)When will an investment of $500 double itself? (a) Choose the correct answer below O B. P(t)=0 067P0 et O C. P(0-Po e 00671 O D. Po- Pt)067 (b) The balance after 3 year is (Type an integer or decimal rounded to two decimal places as needed) (c) The doubling time is year. (Type an integer or decimal rounded to two decimal places as needed.) Click to select your answer(s). ON

Solution

dP/dt= 0.067P(t)

dP/P(t)= 0.067 dt

Integrating both sides

ln(P(t))= 0.067t +C

P(t)= C e^0.067t

at t=0, C=P₀

Therefore we get

P(t)= P₀e^0.067t

option c

b. t=3

P(3)= 500e^0.067(3)=$611.31

c. 2P₀=P₀e^0.067t

ln 2= 0.067t

t=10.35