$A$ radioactive substance has a half-life of $h \ days$. Its initial decay rate is given by (Note that at $t = 0, M = m_0$):

If the population grows at the rate $5 \%$ per year,then the time taken for the population to become double is $\quad$ (Given $\log 2 = 0.6912$) (in $years$)

$A$ spherical rain drop evaporates at a rate proportional to its surface area. If initially its radius is $3 \ mm$ and after $1 \ second$ it is reduced to $2 \ mm$,then at any time $t$ its radius is (where $0 \leq t < 3$)

In a bank,the principal increases continuously at the rate of $6 \%$ per year. Then the time required to double $₹ 6000$ is (in years)

The population of a city increases at a rate proportional to the population at that time. If the population of the city increases from $20$ lakhs to $40$ lakhs in $30$ years,then after another $15$ years,the population is:

If it is mentioned that for a curve passing through $(3,4)$,the slope of the curve at any point is the reciprocal of twice the ordinate of that point,then that curve is a