T = 0: N = 1000*2^0 = 1000.
T = 1/2hr: N = 1000*2^1 = 2000.
T = 1hr: N = 1000*2^2 = 4000.
NOTE: The exponent is always equal to
2T.
A. Eq: N = 1000*2^2T.
B. 2T = 2*2 = 4.
N = 1000*2^4 = 16000 Bacteria cells.
A. Find the defining equation for the number N of bacteria in culture after T hours, assuming that no bacteria die.
B. How many bacteria cells are present after 2 hours?
T = 1/2hr: N = 1000*2^1 = 2000.
T = 1hr: N = 1000*2^2 = 4000.
NOTE: The exponent is always equal to
2T.
A. Eq: N = 1000*2^2T.
B. 2T = 2*2 = 4.
N = 1000*2^4 = 16000 Bacteria cells.
The formula for exponential growth is given by:
N = N0 * (2^(T / t))
where:
N is the final number of bacteria
N0 is the initial number of bacteria
T is the time in hours
t is the time it takes for the population to double
In this case, since the bacteria double every half-hour, t = 0.5 hours.
Plugging in the values, the equation becomes:
N = 1000 * (2^(T / 0.5))
B. To find out how many bacteria cells are present after 2 hours, we can substitute T = 2 into the equation:
N = 1000 * (2^(2 / 0.5))
Calculating this equation will give the number of bacteria cells present after 2 hours.
Let's break down the problem step by step:
First, we know that the initial number of bacteria is 1000.
Since the bacteria double every half-hour, we can determine the growth rate as follows:
- After half an hour, there will be 1000 * 2 = 2000 bacteria.
- After another half-hour (1 hour in total), there will be 2000 * 2 = 4000 bacteria.
- After another half-hour (1.5 hours in total), there will be 4000 * 2 = 8000 bacteria.
From this pattern, we can determine the general equation for the number of bacteria after T hours:
N = 1000 * 2^(2T)
In this equation, N represents the number of bacteria and T represents the number of hours passed.
B. To find the number of bacteria after 2 hours, we can substitute T = 2 into the equation:
N = 1000 * 2^(2*2)
= 1000 * 2^4
= 1000 * 16
= 16,000
Therefore, after 2 hours, there will be 16,000 bacteria cells present in the culture.