complete the sentences. there are approximately 3,000 bass in a lake. the population grows at a rate of 2%…

Explanation:

Step1: Use compound - interest formula for population growth

The formula for compound growth is $P = P_0(1 + r)^t$, where $P_0$ is the initial population, $r$ is the growth rate, and $t$ is the number of years. Here, $P_0=3000$ and $r = 0.02$.

Step2: Calculate population at Year 1

$P_1=3000\times(1 + 0.02)^1=3000\times1.02 = 3060$

Step3: Calculate population at Year 4

$P_4=3000\times(1 + 0.02)^4=3000\times1.02^4\approx3000\times1.08243216=3247.3$

Step4: Calculate average rate of change from Year 1 to Year 4

The average rate of change formula is $\frac{\Delta P}{\Delta t}=\frac{P_4 - P_1}{4 - 1}$. So, $\frac{3247.3-3060}{3}=\frac{187.3}{3}\approx62.4$

Step5: Calculate population at Year 5

$P_5=3000\times(1 + 0.02)^5=3000\times1.02^5\approx3000\times1.1040808032 = 3312.2$

Step6: Calculate population at Year 8

$P_8=3000\times(1 + 0.02)^8=3000\times1.02^8\approx3000\times1.171659381 = 3515.0$

Step7: Calculate average rate of change from Year 5 to Year 8

The average rate of change formula is $\frac{\Delta P}{\Delta t}=\frac{P_8 - P_5}{8 - 5}$. So, $\frac{3515.0 - 3312.2}{3}=\frac{202.8}{3}=67.6$

Answer:

From Year 1 to Year 4, the average rate of change of the population was about $62.4$ bass per year. From Year 5 to Year 8, the average rate of change of the population was about $67.6$ bass per year.