Final answer:
Per capita earnings as a function of time requires knowledge of how earnings and population change over time, often modeled with exponential growth functions. Without specific growth rates or models, a precise per capita earnings function cannot be provided.
Step-by-step explanation:
To express the per capita earnings (p) of a country as a function of time (t), where e represents earnings and p is the population, one would typically require a formula or data that links earnings (e) and population (p) with the variable time (t). If we assume a model where earnings and population grow at a constant rate over time, we could potentially express per capita earnings as a function of time, but specific rates of change or a model would be needed for a precise formulation.
For example, if earnings e grow according to an exponential function of time and population p also grows exponentially, you would have e(t) = e_0 * e^(rt) and p(t) = p_0 * e^(gt), where r is the rate of growth of earnings, g is the rate of growth of population, and e_0 and p_0 are the initial values at t=0. Thus, the per capita earnings function would be p(t) = (e_0 * e^(rt))/(p_0 * e^(gt)), which simplifies to p(t) = (e_0/p_0) * e^((r-g)t).