Acertain 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?

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.

step-by-step explanation: