Question

A village experienced 2% population growth, compounded continuously, each year for 10 years. At the end of the 10 years, the population was 158.
1. What was the population of the village at the beginning of the 10 years according to the exponential growth function? Round your answer up to the next whole number, and do not include units.

Answer 1

Answer:

The initial population at the beginning of the 10 years was 129.

Step-by-step explanation:

The population of the village may be modeled by the following function.

$P(t) = P_{0}e^{rt}$

In which P is the population after t hours, $P_{0}$ is the initial population and r is the growth rate, in decimal.

In this problem, we have that:

$P(10) = 158, r = 0.02$.

So

$158 = P_{0}e^{0.02*10}$

$P_{0} = 158*e^{-0.2}$

$P_{0} = 129$

The initial population at the beginning of the 10 years was 129.

Answer 2

Answer:

Step-by-step explanation:

The formula representing the population growth after t years can be expressed as

A = P(1+r/n)^nt

Where

A is the population of the village after t years.

P represents the initial population of the village at the beginning of the 10 years.

r represents population growth rate

n represents the number of times that the population was compounded in each year.

From the given information,

A = 158

r = 2% = 2/100 = 0.02

t = 10 years

n = 1 because it was compounded continuously each year.

Therefore

158 = P(1+0.02/1)^1×10

158 = P(1.02)^10

P = 158/(1.02)^10 = 129.615

Approximately 130 to the nearest whole number.