Chapter 5, Problem 36T

Business: stock growth. The growth rate of Fabric Industries stock, in dollars per month, can be modeled by

$\frac{dV}{dt}=k\left(L-V\right),$ where V is the value of a share, in dollars, after t months; $L=\$36,$ the limiting value of the stock; k is a constant; and $V\left(0\right)=0$.

a. Express the solution $V\left(t\right)$

in terms of L and k.

b. If $V\left(6\right)=18,$ determine k to the nearest hundredth.

c. Rewrite $V\left(t\right)$ in terms of t and k using the value of k found in part (b).

d. Use the equation in part (c) to find $V\left(12\right),$ the value of the stock after 12 months.

e. In how many months will the value be $30?