The number of bacteria in a certain population increases according to an exponential growth model, with a growth rate of 11% per hour. An initial sample is obtained from this population, and after four hours, the sample has grown to 4130 bacteria. Find the number of bacteria in the initial sample. Round your answer to the nearest integer.

db/dt = 0.11 b

db/b = .11 dt
ln b = .11t + c'
b = e^(.11 t + c') = C e^.11t)
where C is b at t = 0
when t = 4
b = 4130 = C e^.44
ln 4130 = ln C + .44
8.33 =ln C + .44
ln C = 7.89
C = 2670

Thanks

To find the number of bacteria in the initial sample, we can use the exponential growth formula:

N(t) = N0 * e^(rt)

Where:
N(t) is the number of bacteria at time t,
N0 is the number of bacteria in the initial sample,
e is the base of the natural logarithm, and
r is the growth rate.

From the given information, we know that:
N(t) = 4130 bacteria after 4 hours,
r = 11% per hour.

To find N0, we need to rearrange the formula and solve for N0.

N(t) = N0 * e^(rt)
Divide both sides by e^(rt):
N(t) / e^(rt) = N0

Using this equation, we can find the number of bacteria in the initial sample:

N0 = N(t) / e^(rt)

Let's substitute the given values:

N0 = 4130 / e^(0.11 * 4)

Now, we can calculate N0 by raising e to the power of (0.11 * 4) using a calculator or any software that has an exponential function.

N0 = 4130 / e^(0.44) ≈ 4130 / 1.5548 ≈ 2657

Rounding to the nearest integer, the number of bacteria in the initial sample is 2657.