Acertain country has $10 billion in paper currency in circulation, and each day $50 million comes into the country's banks. the government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. let x(t) denote the amount of new currency (in billions of dollars) in circulation at time t (in days), with x(0) = 0. then dx/dt=(fraction of currency that is old)(0.05billion$/day)
so
dx/dt=((10-x)/10)*(0.05)=0.005(10-x )

with this info, determine x(t) by solving the differential equation and using the initial condition x(0)=0

my initial answer was 1000(1-e^-t/200) but that was incorrect

Step-by-step explanation:

The differential equation

can be solved by separation of variables. Write the equation as

Integrate on both sides

where C is a constant.

is also a constant and we will keep calling it C, (there is no reason to change the letter). We have then

(1/C) is a constant, and for the same reason we will keep calling it C. So the general solution is

Now, we use the initial condition x(0)=0

and the particular solution is

70,000 + 6,000 + 800 + 30

step-by-step explanation:

34.5 cm

step-by-step explanation:

generally for a circular segment of angle, θ° and radius r

arc length

= (θ/360) x circumference

= (θ/360) x 2πr

in our case, θ = 60°, π=3.142 and r = 33 cm

substitute into above formula

arc length

= (60/360) x 2(3.142)( 33) = 34.5 cm