a trout population grew from 4 in 1992 to 16 in 1993 and then to 64 in 1994. if it continued to grow…

Answer:

C. 256

Explanation:

Step1: Identify growth - factor

The population grows from 4 in 1992 to 16 in 1993. The growth - factor $r=\frac{16}{4} = 4$.

Step2: Check exponential growth

From 1993 (population = 16) to 1994 (population = 64), $\frac{64}{16}=4$. So the population growth follows the formula $P(t)=P_0r^{t - t_0}$, where $P_0$ is the initial population, $r$ is the growth - factor, and $t$ is the time.

Step3: Calculate population in 1995

In 1994, the population $P(1994)=64$ and $r = 4$. For 1995 ($t = 1995$, $t_0=1994$), using the formula $P(1995)=P(1994)\times r$. Substitute $P(1994) = 64$ and $r = 4$ into the formula: $P(1995)=64\times4=256$.