Answer:
C. 1.8027
Step-by-step explanation:
The exponential population growth model is given by:
[tex]P(t) = P_{0}e^{rt}[/tex]
In which P(t) is the population after t years, [tex]P_{0}[/tex] is the initial population and r is the growth rate.
At the beginning of a population study, the population of a large city was 1.65 million people. Three years later, the population was 1.74 million people.
This means that [tex]P_{0} = 1.65, P(3) = 1.74[/tex]
Applying this to the equation, we find r. So
[tex]P(t) = P_{0}e^{rt}[/tex]
[tex]1.74 = 1.65e^{3r}[/tex]
[tex]e^{3r} = \frac{1.74}{1.65}[/tex]
[tex]e^{3r} = 1.0545[/tex]
Applying ln to both sides
[tex]\ln{e^{3r}} = \ln{1.0545}[/tex]
[tex]3r = \ln{1.0545}[/tex]
[tex]r = \frac{\ln{1.0545}}{3}[/tex]
[tex]r = 0.0177[/tex]
So
[tex]P(t) = 1.65e^{0.0177t}[/tex]
What would be the population of the city 5 years after the start of the population study?
This is P(5).
[tex]P(t) = 1.65e^{0.0177t}[/tex]
[tex]P(5) = 1.65e^{0.0177*5}[/tex]
[tex]P(5) = 1.8027[/tex]
So the correct answer is:
C. 1.8027
