Bacteria colonies can increase by 32% every day. If you started with 150 bacteria microorganisms, how large would the colony be after 8 days?
Future Amount $=I(1+r)^t$
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Round your answer to the nearest whole number.
Answer (2)
Identify the initial amount I = 150 , the rate of increase r = 0.32 , and the time period t = 8 .
Substitute the values into the formula: Future Amount = 150 ( 1 + 0.32 ) 8 .
Calculate the future amount: Future Amount = 150 × ( 1.32 ) 8 = 1382.555928075633 .
Round the future amount to the nearest whole number: 1383 .
Explanation
Understanding the Problem We are given that bacteria colonies increase by 32% every day. We start with 150 bacteria microorganisms and want to find out how large the colony will be after 8 days. 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 period. We need to round the answer to the nearest whole number.
Identifying the Given Values First, we identify the given values:
Initial amount, I = 150
Rate of increase, r = 32% = 0.32
Time period, t = 8 days
Substituting the Values into the Formula Now, we substitute these values into the formula:
Future Amount = 150 ( 1 + 0.32 ) 8
Calculating the Future Amount Next, we calculate the future amount:
Future Amount = 150 ( 1.32 ) 8
Future Amount = 150 × 9.21703952050422
Future Amount = 1382.555928075633
Rounding to the Nearest Whole Number Finally, we round the future amount to the nearest whole number:
Future Amount ≈ 1383
Final Answer Therefore, after 8 days, the bacteria colony would be approximately 1383 microorganisms.
Examples
Understanding exponential growth, like that of a bacteria colony, is crucial in various real-world scenarios. For instance, in epidemiology, it helps predict the spread of infectious diseases, allowing healthcare professionals to implement timely interventions. Similarly, in finance, compound interest follows a similar exponential growth pattern, enabling investors to estimate the future value of their investments. By grasping these concepts, one can make informed decisions in healthcare, finance, and other fields where exponential growth plays a significant role. For example, if you invest $1000 at an annual interest rate of 5%, after 10 years, your investment would grow to $1000(1+0.05)^{10} \approx $1628.89.
After 8 days, a bacteria colony starting with 150 microorganisms and increasing by 32% daily will grow to approximately 1383 microorganisms. This is calculated using the formula for exponential growth. The final value is rounded to the nearest whole number.
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