Question

According to the Bureau of Labor Statistics total nonfarm employment in the Houston-The Woodlands-Sugar Land Metropolitan Statistical Area stood at 2 million jobs in September 2015, up 35,500, or 1.2 percent, from one year earlier. If the trend continues, give an exponential function that describes the number of jobs in Houston area in t year.

Answer 1

Let the exponential function that describes the number of jobs in Houston area in t year (from 2014) be J(t) = ab^t where a, b are arbitrary real numbers

When t = 0, we have J(0) = 2000000 so that 2000000 = ab⁰ or, a = 2000000. Then J(t) = 2000000b^t.

Further, in 2015, when t = 1, we have J(1) = 2035500 so that 2035500 = 2000000b. Hence, b = 2035500/2000000 = 4071/400.

Thus, J(t) = 2000000*(4071/4000)^t.

This is the exponential function that describes the number of jobs in Houston area in t years.