Question

The consumption of natural gas by a company satisfies the empirical equation V=1.50t+0.008t^2, where V is the volume in millions of cubic feet and t the time in months. Express this equation in units of cubic feet and seconds. Put the proper units on the coefficients. Assume that a month is 30 days.


The original empirical equation means
V (ft^3) = 10^6 * [ 1.5 ft^3/month * t(month) + 0.008 ft^3/month^2 * t^2 (month^2)]

It t is to be in seconds, you need to make some conversions of the coefficients, using 1 month = 2.592*10^6 s

The coefficient of t is 1.5 ft^3/month * (1 month/2.592*10^6 s) = 5.79*10^-7 ft^3/s

The coefficient of t^2 is
0.008 ft^3/month^2 * (1 month^2/6.72*10^12 s^2) = 1.19*10^-15 ft^3/s^2

So you can rewrite the equation as
V (ft^3) = 0.579 ft^3/s * t
+ 1.19*10^-9 ft^3/s^2 * t^2

when t is in seconds.


thank you so much!!