the count of bacteria in a culture was 525000. if it is increasing at the rate of 3 1/2% per hour find the count of bacteria at the end of 2 hours.
To find the count of bacteria at the end of 2 hours, you can use the formula for exponential growth:
A = P(1 + r)^t
Where:
- A is the final count of bacteria
- P is the initial count of bacteria
- r is the growth rate as a decimal
- t is the time in hours
Given:
P = 525000 (initial count of bacteria)
r = 3.5% or 0.035 (growth rate per hour)
t = 2 (time in hours)
Substituting the values into the formula:
A = 525000(1 + 0.035)^2
A ≈ 525000(1.035)^2
A ≈ 525000(1.0711225)
A ≈ 561,088.26
Therefore, the count of bacteria at the end of 2 hours is approximately 561,088.
To find the count of bacteria at the end of 2 hours, we will need to calculate the growth rate for each hour and then apply it to the initial count.
Step 1: Calculate the growth rate per hour.
Given that the bacteria is increasing at a rate of 3 1/2% per hour, we can convert it into decimal form:
3 1/2% = 3.5% = 0.035
So, the growth rate per hour is 0.035.
Step 2: Calculate the count of bacteria at the end of 1 hour.
To find the count at the end of 1 hour, we need to add the growth to the initial count.
Count at the end of 1 hour = Initial count + (Initial count * growth rate)
Count at the end of 1 hour = 525000 + (525000 * 0.035)
Step 3: Calculate the count of bacteria at the end of 2 hours.
To find the count at the end of 2 hours, we need to repeat the calculation from step 2.
Count at the end of 2 hours = Count at the end of 1 hour + (Count at the end of 1 hour * growth rate)
Count at the end of 2 hours = (525000 + (525000 * 0.035)) + ((525000 + (525000 * 0.035)) * 0.035)
Now, let's calculate the count at the end of 2 hours:
Count at the end of 1 hour = 525000 + (525000 * 0.035)
Count at the end of 1 hour = 525000 + 18375
Count at the end of 1 hour = 543375
Count at the end of 2 hours = 543375 + (543375 * 0.035)
Count at the end of 2 hours = 543375 + 19018.125
Count at the end of 2 hours ≈ 562393.125
Therefore, the count of bacteria at the end of 2 hours is approximately 562,393.
Bakwas
525,000 * 1.035 = 543,375
543,375 * 1/045 = ?