Derivative word problem The number of households in a certai

Derivative word problem

The number of households in a certain community is given by: h(t) = 1.26^2*t +7800 households t years after 2001.

The proportion (expressed as a decimal) of the households in this same community that have DVD recorders is given by: p(t) =0.663/(1 + 3781e^(1.875t)), t years after 2001.

What does C(t) = h(t)p(t) represent and what does C\'(t) represent.

Solution

The number of households in the community is given by : h(t) = 1.26^2*t +7800.

The proportion of households that have DVD players is given by : p(t) = 0.663/(1 + 3781e^(1.875t))

C(t) = h(t)*p(t) gives the number of households that have a DVD player in any year t, where t is the number of years after 2001.

C\'(t) is the rate of change of the number of households with a DVD player.

C(t) is the number of households with a DVD player and C\'(t) is the rate of change in the number of households with a DVD player.