In a experiment the count of bacteria was increasing at the rate of 2.5% per hour. Initially, the count was 512000.Find the bacteria at the end of 2 hours?
count = 512000(1.025)^2
= .....
To find the count of bacteria at the end of 2 hours, we can use the formula for exponential growth:
Final Value = Initial Value * (1 + Growth Rate/100) ^ Number of time periods
In this case, the initial value is 512,000, the growth rate is 2.5%, and the number of time periods is 2 (for 2 hours).
Substituting these values into the formula, we have:
Final Value = 512,000 * (1 + 2.5/100) ^ 2
Calculating the value inside the parentheses first: 2.5/100 = 0.025, and adding 1 gives 1.025.
Substituting this into the formula:
Final Value = 512,000 * (1.025) ^ 2
Simplifying further:
Final Value = 512,000 * 1.050625
Performing the multiplication:
Final Value = 537,081.6
Therefore, the count of bacteria at the end of 2 hours is approximately 537,082.
You can use the formula for exponential growth to solve similar problems. Just substitute the given values into the formula and simplify the expression step by step to find the final value.