Question

The population, P, of a town after t years is represented using the equation. Which of the following is an equivalent expression?

(a) Open-ended response
(b) P × t
(c) P/t
(d) P + t

Answer 1

The equivalent expression for the population P of a town after t years captures exponential growth, which cannot be reduced to the simple alternatives of P multiplied by, divided by, or added to t.

Step-by-step explanation:

Given the various equations representing population growth, the equivalent expression for the population, P, of a town after t years is not simply P multiplied by t, P divided by t, or P added to t. The population growth is typically modeled using an exponential function to accommodate the compound growth aspect. For example, P = Poer(t-to), where Po is the initial population at the starting time to, r is the growth rate, and e is the base of the natural logarithm. Similarly, the expression P = Poeln(1+p)(t-to) shows a compounded growth rate p over time. Therefore, an equivalent expression for the population after t years is one that reflects this exponential growth, not a linear relationship like those presented in options b, c, and d.