Answer:
(a) To find an exponential model of the form n(t) = n0 * 2^(t/a) for the population t years after 2014, we need to determine the value of "a" which represents the doubling time.
Given that the observed doubling time is 19 years, we can substitute the values into the equation:
19 = a
Therefore, the exponential model for the population t years after 2014 is:
n(t) = 195,000 * 2^(t/19)
(b) To find an exponential model of the form n(t) = n0 * e^(rt) for the population t years after 2014, we need to determine the value of "r" which represents the growth rate.
The doubling time "a" can be related to the growth rate "r" by the formula:
a = ln(2) / r
Substituting the value of "a" as 19, we can solve for "r":
19 = ln(2) / r
19r = ln(2)
r = ln(2) / 19
Rounding the value of "r" to four decimal places, we get:
r ≈ 0.0366
Therefore, the exponential model for the population t years after 2014 is:
n(t) = 195,000 * e^(0.0366t)
Please note that these models assume continuous exponential growth and do not take into account other factors that may affect population growth.