Question

A certain species of fish is to be introduced into a lake, and wildlife experts estimate the population will grow to P(t)= (771)4^ t/3, where trepresents the number of years from the time of introduction.What is the quadrupling-time for this population of fish?

Answer 1

Analyzing the function, we can see that the initial value of the function is 771 (f(0) = 771).

Also, this value will be multiplied by 4 when its exponent is equal to 1.

Since the exponent of 4 is equal to t/3, let's equate the exponent to 1:

$\begin{gathered} \frac{t}{3}=1 \\ t=3\cdot1 \\ t=3 \end{gathered}$

Therefore, when t = 3, the initial value of 771 will be multiplied by 4.

Also, for each increase of 3 years, the population will be multiplied by 4, since the exponent increases by 1.

So the answer is 3 years.