Question

a lake initially contains 2500 fish. suppose that in the absence of predators or other causes of removal, the fish population increases by 7% each month. however, factoring in all causes, 400 fish are lost each month. how many fish will be in the pond after 7 months?

Answer 1

To calculate the fish population in the pond after 7 months, we apply a 7% monthly growth rate and subtract a loss of 400 fish each month. After performing these calculations for seven consecutive months, the population of fish will decrease to 1179.

Step-by-step explanation:

To determine the fish population in the pond after 7 months, we need to consider both the monthly growth rate and the monthly loss. The population increases by 7% each month, but we also have a loss of 400 fish each month.

We can represent the growth by multiplying the current population by 1.07 (100% + 7% growth) and then subtract the 400 fish that are lost to get the population for the next month.

1. Initial population = 2500 fish.
2. Monthly growth rate = 7%, represented as a multiplication factor of 1.07.
3. Monthly loss = 400 fish.
4. Population for month 1 = (2500 x 1.07) - 400.
5. Repeat the above calculation for each subsequent month using the population from the previous month instead of 2500.

Let's do the calculation for the first month. For the first month: Population = (2500 x 1.07) - 400 = 2675 - 400 = 2275 fish.

Now, we will repeat this process for each month, always using the new population number from the previous month. After calculating for seven months, we will have the final population number.

After 7 months of growth and loss, the fish population in the pond will be:

• Month 1: 2275 fish
• Month 2: 2042 fish
• Month 3: 1835 fish
• Month 4: 1645 fish
• Month 5: 1474 fish
• Month 6: 1318 fish
• Month 7: 1179 fish