Answer:
To find the number of bacteria after 1 hour, we need to use the formula P = P0 * e^(kt), where P is the final number of bacteria, P0 is the initial number of bacteria, t is the time in hours, and k is a constant.
Given that there are 1000 bacteria at the start (P0 = 1000) and after 10 minutes (t = 10/60 = 1/6 hours), the number of bacteria becomes 2000, we can substitute these values into the formula and solve for k.
2000 = 1000 * e^(k * 1/6)
Dividing both sides by 1000:
2 = e^(k/6)
To isolate e^(k/6), we take the natural logarithm (ln) of both sides:
ln(2) = k/6
Now, we can solve for k by multiplying both sides by 6:
k = 6 * ln(2)
Now that we have the value of k, we can use it to find the number of bacteria after 1 hour (t = 1):
P = P0 * e^(kt)
P = 1000 * e^(6 * ln(2) * 1)
P = 1000 * e^(6 * ln(2))
P ≈ 1000 * 2.718^(6 * 0.693)
P ≈ 1000 * 2.718^4.158
P ≈ 1000 * 64.498
P ≈ 64,498
Therefore, there will be approximately 64,498 bacteria after 1 hour.
Step-by-step explanation: