We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

\(\displaystyle p(t)=p_0e^{kt}\)

Where \(\displaystyle p_0\) is an initial population value, \(\displaystyle t\)  represents a measure of elapsed time relative to this population value, and \(\displaystyle k\) is the constant of proportionality.

Since the population decreased from 15800 to 2400 between 3:00 and 5:00, we can solve for this constant of proportionality:

\(\displaystyle 2400=15800e^{k(5-3)}\)

\(\displaystyle \frac{12}{79}=e^{2k}\)

\(\displaystyle 2k=ln(\frac{12}{79})\)

\(\displaystyle k=\frac{ln(\frac{12}{79})}{2}=-0.942\)

Now that the constant of proportionality is known, we can use it to find an expected population value relative to an initial population value due to the difference in time points. Convert minutes to decimals by dividing by 60:

\(\displaystyle P=2400e^{(-0.942)(5.5-5)} \approx 1499\)

We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

\(\displaystyle p(t)=p_0e^{kt}\)

Where \(\displaystyle p_0\) is an initial population value, \(\displaystyle t\)  represents a measure of elapsed time relative to this population value, and \(\displaystyle k\) is the constant of proportionality.

Since the population decreased from 1100 to 85 between 1993 and 2013, we can solve for this constant of proportionality:

\(\displaystyle 85=1100e^{k(2013-1993)}\)

\(\displaystyle \frac{17}{220}=e^{10k}\)

\(\displaystyle 10k=ln(\frac{17}{220})\)

\(\displaystyle k=\frac{ln(\frac{17}{220})}{10}=-0.256\)

Now that the constant of proportionality is known, we can use it to find an expected population value relative to an initial population value due to the difference in time points:

\(\displaystyle P=85e^{(-0.256)(2015-2013)} \approx 51\)

We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

\(\displaystyle p(t)=p_0e^{kt}\)

Where \(\displaystyle p_0\) is an initial population value, \(\displaystyle t\)  represents a measure of elapsed time relative to this population value, and \(\displaystyle k\) is the constant of proportionality.

Since the population increased from 43800 to 87215 between 1990 and 1995, we can solve for this constant of proportionality:

\(\displaystyle 87215=43800e^{k(1995-1990)}\)

\(\displaystyle \frac{87215}{43800}=e^{5k}\)

\(\displaystyle 5k=ln(\frac{87215}{43800})\)

\(\displaystyle k=\frac{ln(\frac{87215}{43800})}{5}=0.138\)

Now that the constant of proportionality is known, we can use it to find an expected population value relative to an initial population value due to the difference in time points:

\(\displaystyle P=87215e^{(0.138)(2015-1995)} \approx 1377983\)

We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

\(\displaystyle p(t)=p_0e^{kt}\)

Where \(\displaystyle p_0\) is an initial population value, \(\displaystyle t\)  represents a measure of elapsed time relative to this population value, and \(\displaystyle k\) is the constant of proportionality.

Since the population increased from 110 to 310 between January and July, we can solve for this constant of proportionality. Use the number of the months as they're ordered in the calendar:

\(\displaystyle 310=110e^{k(7-1)}\)

\(\displaystyle \frac{31}{11}=e^{6k}\)

\(\displaystyle 6k=ln(\frac{31}{11})\)

\(\displaystyle k=\frac{ln(\frac{31}{11})}{6}=0.173\)

Now that the constant of proportionality is known, we can use it to find an expected population value relative to an initial population value due to the difference in time points:

\(\displaystyle P=310e^{(0.173)(10-7)} \approx 521\)

We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

\(\displaystyle p(t)=p_0e^{kt}\)

Where \(\displaystyle p_0\) is an initial population value, \(\displaystyle t\)  represents a measure of elapsed time relative to this population value, and \(\displaystyle k\) is the constant of proportionality.

Since the population increased from 1500 to 5800 between 2013 and 2015, we can solve for this constant of proportionality:

\(\displaystyle 5800=1500e^{k(2015-2013)}\)

\(\displaystyle \frac{58}{15}=e^{2k}\)

\(\displaystyle 2k=ln(\frac{58}{15})\)

\(\displaystyle k=\frac{ln(\frac{58}{15})}{2}=0.676\)

Now that the constant of proportionality is known, we can use it to find an expected population value relative to an initial population value due to the difference in time points:

\(\displaystyle P=5800e^{(0.676)(2018-2015)} \approx 44074\)

We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

\(\displaystyle p(t)=p_0e^{kt}\)

Where \(\displaystyle p_0\) is an initial population value, \(\displaystyle t\)  represents a measure of elapsed time relative to this population value, and \(\displaystyle k\) is the constant of proportionality.

Since the population increased from 1200  to 58000 between 2189 and 2213, we can solve for this constant of proportionality:

\(\displaystyle 58000=1200e^{k(2213-2189)}\)

\(\displaystyle \frac{145}{3}=e^{24k}\)

\(\displaystyle 24k=ln(\frac{145}{3})\)

\(\displaystyle k=\frac{ln(\frac{145}{3})}{24}=0.1616\)

Now that the constant of proportionality is known, we can use it to find an expected population value relative to an initial population value due to the difference in time points:

\(\displaystyle P=58000e^{(0.1616)(2225-2213)} \approx 403285\)

We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

\(\displaystyle p(t)=p_0e^{kt}\)

Where \(\displaystyle p_0\) is an initial population value, \(\displaystyle t\)  represents a measure of elapsed time relative to this population value, and \(\displaystyle k\) is the constant of proportionality.

Since the population increased from 1100 to 5300 between 3:30 and 3:15, we can solve for this constant of proportionality. Treat the minutes as decimals of an hour by dividing by 60:

\(\displaystyle 5300=1100e^{k(3.5-3.25)}\)

\(\displaystyle \frac{53}{11}=e^{0.25k}\)

\(\displaystyle 0.25k=ln(\frac{53}{11})\)

\(\displaystyle k=\frac{ln(\frac{53}{11})}{0.25}=6.290\)

Now that the constant of proportionality is known, we can use it to find the specified point in time:

\(\displaystyle 200000=5300e^{6.290(t-3.5)}\)

\(\displaystyle 6.290(t-3.5)=ln(\frac{2000}{53})\)

\(\displaystyle t=3.5+\frac{ln(\frac{2000}{53})}{6.290}=4.077 \rightarrow 4:05\)

We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

\(\displaystyle p(t)=p_0e^{kt}\)

Where \(\displaystyle p_0\) is an initial population value, \(\displaystyle t\)  represents a measure of elapsed time relative to this population value, and \(\displaystyle k\) is the constant of proportionality.

Since the population increased from 24 to 313 between 3:00 and 4:00, we can solve for this constant of proportionality:

\(\displaystyle 313=24e^{k(4-3)}\)

\(\displaystyle \frac{313}{24}=e^{k}\)

\(\displaystyle k=ln(\frac{313}{24})=2.568\)

Now that the constant of proportionality is known, we can use it to find the specified point in time:

\(\displaystyle 50000=313e^{2.568(t-4)}\)

\(\displaystyle 2.568(t-4)=ln(\frac{50000}{313})\)

\(\displaystyle t=4+\frac{ln(\frac{50000}{313})}{2.568} =5.976 \rightarrow 5:59\)

We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

\(\displaystyle p(t)=p_0e^{kt}\)

Where \(\displaystyle p_0\) is an initial population value, \(\displaystyle t\)  represents a measure of elapsed time relative to this population value, and \(\displaystyle k\) is the constant of proportionality.

Since the population increased from 11 to 165 between 1:00 and 3:00, we can solve for this constant of proportionality:

\(\displaystyle 165=11e^{k(3-1)}\)

\(\displaystyle 15=e^{2k}\)

\(\displaystyle 2k=ln(15)\)

\(\displaystyle k=\frac{ln(15)}{2}=1.354\)

Now that the constant of proportionality is known, we can use it to find the specified point in time:

\(\displaystyle 800000=165e^{1.354(t-3)}\)

\(\displaystyle 1.354(t-3)=ln(\frac{160000}{33})\)

\(\displaystyle t=3+\frac{ln(\frac{160000}{33})}{1.354}=9.268 \rightarrow 9:16\)

We're told that the rate of change of the population is proportional to the population itself, meaning that this problem deals with exponential growth/decay. The population can be modeled thusly:

\(\displaystyle p(t)=p_0e^{kt}\)

Where \(\displaystyle p_0\) is an initial population value, and \(\displaystyle k\) is the constant of proportionality.

Since the population increased from 12000 to 96000 between 2011 and 2015, we can solve for this constant of proportionality:

\(\displaystyle 96000=12000e^{k(2015-2011)}\)

\(\displaystyle 8=e^{4k}\)

\(\displaystyle 4k=ln(8)\)

\(\displaystyle k=\frac{ln(8)}{4}=0.520\)