Question

An island population of 20,000, grows by 5% each year, compounded continuously. How many inhabitants will the island have in 5 years according to the exponential growth function?

Answer 1

Answer:

Step-by-step explanation:

Initial population of people living in the island is 20,000

P = 20,000

It was compounded annually. This means that it was compounded once in a year. So

n = 1

The rate at which the population was compounded is 5%. So

r = 5/100 = 0.05

It was compounded for 5 years. So

t = 1

the exponential growth function is expressed as

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

A = total population in the island at the end of t years. Therefore

A = 20000 (1+0.05/1)^1×5

A = 20000×1.2762815625

A = 25525.63125

The number of inhabitants that the island will have after 5 years is approximately 25526 people

Answer 2

Answer:

25680

Step-by-step explanation:

A=Pe^rt

A=20000e^((0.05)(5))

A=20000e^(.25)

A=25680.508