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.
