Calculating the Size of a Penguin Population after 6 Years Using Exponential Growth Formula

Initial population of 600 penguins triples in size each year for six years. Find size of population after six years

To find the size of the penguin population after six years, we can use the formula for exponential growth:

P = P₀ * (1 + r)^t

Where:
P is the final population
P₀ is the initial population
r is the growth rate (in decimal form)
t is the number of years

Given:
Initial population (P₀) = 600
Growth rate (r) = 3 (since it triples in size each year)
Number of years (t) = 6

Substituting these values into the formula, we have:

P = 600 * (1 + 3)^6

To simplify the calculation, let’s first find the value inside the brackets:

(1 + 3)^6 = 4^6 = 4096

Now, substituting this value back into the formula:

P = 600 * 4096

Calculating this multiplication:

P = 2,457,600

Therefore, the size of the penguin population after six years would be 2,457,600

To find the size of the penguin population after six years, we can use the formula for exponential growth:

P = P₀ * (1 + r)^t

Where:
P is the final population
P₀ is the initial population
r is the growth rate (in decimal form)
t is the number of years

Given:
Initial population (P₀) = 600
Growth rate (r) = 3 (since it triples in size each year)
Number of years (t) = 6

Substituting these values into the formula, we have:

P = 600 * (1 + 3)^6

To simplify the calculation, let’s first find the value inside the brackets:

(1 + 3)^6 = 4^6 = 4096

Now, substituting this value back into the formula:

P = 600 * 4096

Calculating this multiplication:

P = 2,457,600

Therefore, the size of the penguin population after six years would be 2,457,600.

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