$A$ spherical balloon expands at a rate proportional to its surface area. Initially, its radius is $2 \text{ cm}$ and $5$ minutes later it increases to $7 \text{ cm}$. What will be the surface area of the spherical balloon after $12$ minutes (in $\text{ cm}^2$)?

The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is $1000$ at initial time $t = 0$. The number of bacteria is increased by $20\%$ in $2$ hours. If the population of bacteria is $2000$ after $\frac{k}{\log_{e}\left(\frac{6}{5}\right)}$ hours,then $\left(\frac{k}{\log_{e} 2}\right)^{2}$ is equal to

The rate of increase of bacteria in a certain culture is proportional to the number present. If it doubles in $5$ hours,then in $25$ hours,its number would be ......... times the original.

In a culture,the bacteria count is $1,00,000$. The number increases by $10 \%$ in $2$ hours. In how many hours will the count reach $2,00,000$,if the rate of growth of bacteria is proportional to the number present?

Radium decomposes at a rate proportional to the amount present at any time. If $P \%$ of the amount disappears in one year,then the amount of radium left after $2$ years is

The rate of increase of bacteria in a culture is proportional to the number of bacteria present at that instant. It is found that the number doubles in $6 \text{ hours}$. The number of bacteria becomes $n$ times the initial number at the end of $18 \text{ hours}$. Find $n$.