Question

HELPPPP!!

The population of a certain town is 158, 260 and increases exponentially at the rate of 6% every year.

Which equation best represents the population after a years?


A.) y = 158, 260(0.06)


B.) y = 158, 260(0.94)-


C.) y = 158, 260(1.06)-


D.) Oy=158,260(1.6)

Answer 1

The best equation to represent the population after a certain number of years with a 6% annual growth rate is y = 158, 260(1.06)a.

Step-by-step explanation:

The equation that best represents the population of a certain town after a years, considering an exponential increase at the rate of 6% every year, is:

y = 158, 260(1.06)

a

This equation uses the exponential growth model, where P represents the future population, Po is the initial population, r is the growth rate in decimal form (e.g., 0.06 for 6%), and t is the time in years.

An exponential growth model is represented by the equation P = Poer(t-to), as per the reference text. Since the town's population is growing at a steady rate without limitations that would create a logistic growth model, we can ignore the effects of population limiting factors.

Option C

is correct because it incorporates the exponential growth factor

(1 + r)

raised to the power of the number of years, denoted by

a.