A country has 10 billion dollars in paper currency in circulation, and each day 35 million dollars 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 bank. Let $x = x(t)$ denote the number of new dollars in circulation after $t$ days with units in billions and $x(0) = 0$.

A. Determine a differential equation which describes the rate at which $x$ is growing:
$\frac{dx}{dt} =$

B. Solve the differential equation subject to the initial conditions given above.
$x(t) =$

C. How many days will it take for the new bills to account for 90 percent of the currency in circulation?