1. The population growth of a small town is modeled

Ответ:

UndeadDelta

30.01.2022

A. Growth rate = r = 0.149

B. P(0) = 6545.52

C. P(11) = 33,709

D. P(39) = 2,185,876

Step-by-step explanation:

The population growth of a small town is modeled by the following function,

$P(t) = 6545.52 e^{0.149t}$

Where 6545.52 is the initial population, 0.149 is the rate of growth of the population and t is the number of years since 1980.

A. What is the growth rate for P(t)?

The growth rate is

Growth rate = r = 0.149

B. What was the population in 1980?

Since t is the number of years since 1980, therefore, t = 0 for the year 1980.

$P(0) = 6545.52 e^{0.149(0)} \\\\ P(0) = 6545.52 e^{0} \\\\ P(0) = 6545.52 \\\\$

C. Find P(11) and explain what it means in the context of the problem.

$P(11) = 6545.52 e^{0.149(11)} \\\\P(11) = 6545.52 e^{1.639} \\\\ P(11) = 6545.52 (5.15) \\\\P(11) = 33,709$

It represents the population of the town after 11 years since 1980.

D. What is the projected population in 2019?

t = 2019 - 1980 = 39 years

$P(39) = 6545.52 e^{0.149(39)} \\\\P(39) = 6545.52 e^{5.811} \\\\ P(39) = 6545.52 (333.95) \\\\P(39) = 2,185,876$

Therefore, the projected population in 2019 is expected to be 2,185,876.

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