Question 184956
Here's one approach:
{{{P(t) = (t^(1/4)+3)^3}}} Expand the right side to get:
{{{P(t) = t^(3/4)+9t^(1/2) + 27t^(1/4)+27}}} Now take the first derivative to find the rate of change of P with respect to t.
{{{dP/dt = (3/4)t^(-1/4)+(9/2)t^(-1/2) + (27/4)t^(-3/4)}}} Simplify this:
{{{dP/dt = (3/4t^(1/4)) + (9/2t^(1/2)) + (27/4t^(3/4))}}} Substitute t = 16.
{{{dP/dt = (3/4(16)^(1/4))+(9/2(16)^(1/2)) + (27/4(16)^(3/4))}}} Evaluate the right side.
{{{dP/dt = (3/8)+(9/8)+(27/32)}}} Add the fractions - the LCD is 32.
{{{dP/dt = (12+36+27)/32}}}
{{{highlight(dP/dt = 75/32)}}}