Question

a trout population grew from 4 in 1992 to 16 in 1993 and then to 64 in 1994. if it continued to grow exponentially, approximately how many trout were there in 1995? 100 128 256 320

Explanation:

Step1: Identify the growth pattern

The population grows from 4 in 1992 to 16 in 1993 (a factor of 4), and from 16 to 64 in 1994 (also a factor of 4). So the growth is exponential with a common - ratio of 4.
Let the initial population $P_0 = 4$ in 1992, and the general formula for exponential growth is $P(t)=P_0r^t$, where $r$ is the common ratio and $t$ is the number of years since 1992. Here $r = 4$.
In 1995, $t = 3$ (since 1995 - 1992=3).

Step2: Calculate the population in 1995

Substitute $P_0 = 4$, $r = 4$, and $t = 3$ into the formula $P(t)=P_0r^t$.
$P(3)=4\times4^3$.
Using the rule of exponents $a^m\times a^n=a^{m + n}$, we have $4\times4^3=4^{1 + 3}=4^4$.
$4^4=256$.

Answer:

256