The doubling period should be calculated using the formula:
doubling time = (ln 2) / r
where r is the exponential growth rate.
Using the given information, we can calculate the exponential growth rate as:
r = (ln N1 - ln N0) / t
where N0 is the initial population, N1 is the final population, and t is the time elapsed. Plugging in the values, we get:
r = (ln 1600 - ln 300) / 35
r = 0.5128
Now we can calculate the doubling period as:
doubling time = (ln 2) / r
doubling time = (ln 2) / 0.5128
doubling time = 1.35 hours (rounded to two decimal places)
Therefore, the doubling period is approximately 1.35 hours.
To find the population after 70 minutes, we can use the formula for exponential growth:
N = N0 * e^(rt)
Plugging in the values, we get:
N = 300 * e^(0.5128 * (70/60))
N = 1467.05
Therefore, the population after 70 minutes is approximately 1467.05.
To find when the population will reach 10000, we can use the same formula again:
N = N0 * e^(rt)
Plugging in the given values, we get:
10000 = 300 * e^(0.5128 * t)
Dividing both sides by 300, we get:
e^(0.5128 * t) = 10000 / 300
e^(0.5128 * t) = 33.3333
Taking the natural logarithm of both sides, we get:
0.5128 * t = ln(33.3333)
t = ln(33.3333) / 0.5128
t = 23.37 hours (rounded to two decimal places)
Therefore, the population will reach 10000 after approximately 23.37 hours.