The annual rate of increase of an investment's value is proportional to its value, specifically 3.5% of the value. V V\,V is the value in thousands of pounds and t t\,t is the time in years.
Write down a differential equation for this relationship.
Show that V=Ae0.035tV = Ae^{0.035t}V=Ae0.035t where A A\,A is a constant.
Given that the initial value of the investment is £12,000. Find the value after 5 years, giving your answer to the nearest £10.
