At time $t$, the radius of a spherical balloon is $r$ cm. The balloon is being inflated so that

Question

At time $t$, the radius of a spherical balloon is $r$ cm. The balloon is being inflated so that the rate of increase of its radius is inversely proportional to the square root of its radius. When $t=1$, $r=4$, and at this instant, the radius is increasing at $1.5$ cm $\mathrm{s}^{-1}$. Form a differential equation and solve for $r$ in terms of $t$. Determine how much air was in the balloon initially?

Accepted Answer

(a) $r = (4.5t + 3.5)^{\frac{2}{3}}$ ; (b) $51.3$.

Differential Equations - Modelling in Real-Life Problems

Differential Equations - Modelling in Real-Life Problems