Question

The value of a famous work of art increases over time according to dA  kA , where t is time in years dt

since 1990, when the artwork was worth $6000. In the year 2000, it sold at auction for $14000.
a) Build a general form of the function A(t), and use that and the above information to determine the

growth constant, k. Round it to 4-decimal places.

b).Write out the fully determined function.

c).Use your function to determine the estimated value of the artwork this year, 2020, rounded to the nearest $1

d).How many years from 1990 until the artwork is worth $200,000?

Answer 1

We are given that dA/dt= Kdt then, by variable separable method, we will solve the given differential equation and with the help of the initial condition A(0)= 6000 and the given condition that A(10)= 14000, we will get the value of K.

Then, the fully determined function A(t) will be found out, as explained in the solution provided below.