The population of a specific type of deep-sea water fish increases by 3% every month. If there are 758 of this type of fish, how many will there be in 8 months?
Future Amount $= I (1+r)^{ t }$
[?] fish
Round your answer to the nearest whole number.
Answer (2)
Identify the initial population I = 758 , rate of increase r = 0.03 , and time period t = 8 months.
Substitute the values into the formula: Future Amount = 758 ( 1 + 0.03 ) 8 .
Calculate the future amount: Future Amount ≈ 960.21 .
Round the future amount to the nearest whole number: 960 .
Explanation
Understanding the Problem We are given that the initial population of the fish is 758, and it increases by 3% every month for 8 months. We need to find the population after 8 months, rounded to the nearest whole number. The formula for future amount is given as Future Amount = I ( 1 + r ) t , where I is the initial amount, r is the rate of increase, and t is the time in months.
Identifying the Values We identify the given values:
Initial population, I = 758 Rate of increase, r = 3% = 0.03 Time period, t = 8 months
Substituting the Values We substitute the values into the formula:
Future Amount = 758 ( 1 + 0.03 ) 8 Future Amount = 758 ( 1.03 ) 8
Calculating the Future Amount We calculate ( 1.03 ) 8 :
( 1.03 ) 8 ≈ 1.26677008144703
Then, we multiply this by the initial population:
Future Amount = 758 × 1.26677008144703 ≈ 960.2117216918132
Rounding the Result We round the future amount to the nearest whole number:
960.2117216918132 ≈ 960
Final Answer Therefore, after 8 months, there will be approximately 960 fish.
Examples
Imagine you are managing a fish farm, and you want to predict the growth of your fish population over a certain period. Using the formula for exponential growth, you can estimate how many fish you will have in the future, which helps you plan for resources, sales, and overall farm management. This type of calculation is also applicable in other areas, such as predicting the growth of investments or the spread of a virus.
Using the exponential growth formula, the future population of the fish after 8 months, starting from 758 and increasing by 3% each month, is approximately 960. After performing the calculations and rounding, we arrive at the final answer of 960 fish. This calculation helps in predicting the growth of populations over time.
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