$A$ wet substance in the open air loses its moisture at a rate proportional to the moisture content. If a sheet,hung in the open air,loses half its moisture during the first hour,then $90 \%$ of the moisture will be lost in ...... hours.

The rate of increase of the population of a city is proportional to the population present at that instant. In the period of $40$ years,the population increased from $30,000$ to $40,000$. At any time $t$,the population is given by $P(t) = (a)(b)^{\frac{t}{40}}$. Then the values of $a$ and $b$ are respectively:

$A$ spherical raindrop evaporates at a rate proportional to its surface area. If its radius originally is $3 \text{ mm}$ and $1 \text{ hour}$ later has been reduced to $2 \text{ mm}$,then the expression of radius $r$ of the raindrop at any time $t$ is (where $0 \leq t < 3$):

The bacteria increases at a rate proportional to the number of bacteria present. If the original number $N$ doubles in $4$ hours,then the number of bacteria in $12$ hours will be: (in $N$)

In a bank,the principal increases continuously at the rate of $5 \%$ per year. In how many years will Rs $1000$ double itself?

Water is drained from a vertical cylindrical tank by opening a valve at the base of the tank. It is known that the rate at which the water level drops is proportional to the square root of water depth $y$,where the constant of proportionality $k > 0$ depends on the acceleration due to gravity and the geometry of the hole. If $t$ is measured in minutes and $k = \frac{1}{15}$,then the time required to drain the tank if the water is $4 \text{ m}$ deep to start with is .......... $\text{min}$.