Calculating the Population Size After 6 Years | Exponential Growth Formula and Calculation Example

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 population after six years, we need to determine how the initial population of 600 penguins triples in size each year for six years

To find the size of the population after six years, we need to determine how the initial population of 600 penguins triples in size each year for six years.

To do this, we will use the formula for exponential growth:

P = P0 * (1 + r)^n

Where:
P is the final population size
P0 is the initial population size
r is the growth rate
n is the number of years

In this case, the initial population size (P0) is 600 penguins, and the growth rate (r) is 3 since the population triples in size each year. The number of years (n) we are considering is 6.

Plugging these values into the formula, we have:

P = 600 * (1 + 3)^6

Now, let us simplify the expression inside the parentheses:

P = 600 * 4^6

To calculate 4^6, we multiply 4 by itself six times:

4^6 = 4 * 4 * 4 * 4 * 4 * 4 = 4096

Substituting this value back into the formula, we have:

P = 600 * 4096

Multiplying these numbers:

P = 2,457,600

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

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