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HACTEHA [7]
3 years ago
14

At the beginning of a population study, the population of a large city was 1.65 million people. Three years later, the populatio

n was 1.74 million people. Assume that population grows according to an uninhibited exponential growth model.
What would be the population of the city 5 years after the start of the population study?

A. 2.1518
B. 1.7683
C. 1.8027
D. 1.8843
F. None of the Above
Mathematics
1 answer:
Maksim231197 [3]3 years ago
6 0

Answer:

C. 1.8027

Step-by-step explanation:

The exponential population growth model is given by:

P(t) = P_{0}e^{rt}

In which P(t) is the population after t years, P_{0} 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 P_{0} = 1.65, P(3) = 1.74

Applying this to the equation, we find r. So

P(t) = P_{0}e^{rt}

1.74 = 1.65e^{3r}

e^{3r} = \frac{1.74}{1.65}

e^{3r} = 1.0545

Applying ln to both sides

\ln{e^{3r}} = \ln{1.0545}

3r = \ln{1.0545}

r = \frac{\ln{1.0545}}{3}

r = 0.0177

So

P(t) = 1.65e^{0.0177t}

What would be the population of the city 5 years after the start of the population study?

This is P(5).

P(t) = 1.65e^{0.0177t}

P(5) = 1.65e^{0.0177*5}

P(5) = 1.8027

So the correct answer is:

C. 1.8027

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