Question

In 2007, (when t = 0), world solar photovoltaic (PV) market installations were 2826 megawatts and were growing exponentially at a continuous rate of 48% per year.†

(a) Define the variables.

Let S be the world solar PV market installations, in megawatts, in the month t, where t represents the number of years before 2007.

Let S be the world solar PV market installations, in megawatts, in the year t, where t represents the current year.    

Let S be the world solar PV market installations, in megawatts, in the year t, where t represents the number of years since 2007.

Let S be the world solar PV market installations, in watts, in the year t, where t represents the number of years before 2007.

Let S be the world solar PV market installations, in megawatts, in the year t, where t represents the number of years before 2007.

(b) Write a differential equation to describe the relationship.

dS

dt

=

  with initial condition S(0) = __________

(b) Solve the differential equation.
S = ____________

Answer 1

(a)

Let S be the world solar PV market installations, in megawatts, in the year t, where t represents the number of years since 2007

(b)

r=48%=0.48

we can set up differential equation as

(when t = 0), world solar photovoltaic (PV) market installations were 2826 megawatts

so,

(c)

now, we can use variable seperable method

we can integrate both sides

we have

now, we can plug it back

and we get

............Answer