A certain species of fish is to be introduced into a lake, and wildlife experts estimate the population will grow to P (t) = (715) 4t4, where t represents the number of years from the time of introduction. Step 1 of 2: What is the quadrupling-time for this population of fish?

Answer: 4 years

A certain species of fish is to be introduced into a lake, and wildlife experts estimate the population will grow to P (t) = (715) 4^ (t/4), where t represents the number of years from the time of introduction. Step 1 of 2: What is the quadrupling-time for this population of fish?

Step-by-step explanation:

Given;

The function P (t) represent the population of the certain species of fish in the lake at time t (in years).

At time t = 0

P (0) = (715) 4^ (0) = 715 * 1 = 715

Since P (0) = 715, for the population to be quadrupled

P (t) = 4 * 715 = 2860

To estimate the time t for P (t) = 2860, we need to equate it to the function P (t).

P (t) = 2860 = (715) 4^ (t/4)

Divide both sides by 715

4 = 4^ (t/4)

hence,

t/4 = 1

t = 4 years.

Therefore, the quadrupling-time for the population of fish is 4 years.