In the beginning, there is 3000 fish in which for some causes every year 20% of d fish die and 1000 are added. So we need to use compound interest formula to find out the equation that we can just substitute d number of year and find out how many fish there will be in that year
To determine the equation using compound interest formula, we need to identify the relevant variables. In this scenario:
P = Initial amount of fish (3000)
r = Growth rate (expressed as a decimal) (20% or 0.20 in this case, as 20% of fish die)
n = Number of times the growth occurs per year (1 time)
t = Number of years
The compound interest formula is typically used to calculate the growth of a monetary investment over time, but in this case, we will modify it to represent the increase or decrease in the number of fish. The modified formula is:
A = P(1 + r)^nt
Here, A represents the final number of fish after t years. To substitute the variables in this formula, follow these steps:
1. Subtract the death rate (r) from 1 to account for the 20% decrease in the fish population: 1 - 0.20 = 0.80.
2. Substitute the values into the formula:
A = 3000(1 + 0.80)^t
This equation enables you to calculate the number of fish after any given number of years by substituting the desired value for t.