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marissa [1.9K]
2 years ago
11

Need help on this problem

Mathematics
1 answer:
faust18 [17]2 years ago
3 0

Using an exponential function, it is found that:

  • For Country A, the doubling time is of 43 years.
  • For Country B, the growth rate is of 1.9% per year.

<h3>What is the exponential function for population growth?</h3>

The exponential function for population growth is given as follows:

P(t) = P(0)e^{kt}

In which:

  • P(t) is the population after t years.
  • P(0) is the initial population.
  • k is the exponential growth rate, as a decimal.
  • t is the time in years.

For Country A, we have that k = 0.016. The doubling time is t for which P(t) = 2P(0), hence:

P(t) = P(0)e^{kt}

2P(0) = P(0)e^{0.016t}

e^{0.016t} = 2

\ln{e^{0.016t}} = \ln{2}

0.016t = \ln{2}

t = \frac{\ln{2}}{0.016}

t = 43 years.

For Country B, P(36) = 2P(0), hence we have to solve for k to find the growth rate.

P(t) = P(0)e^{kt}

2P(0) = P(0)e^{36k}

e^{36k} = 2

\ln{e^{36k}} = \ln{2}

36k = \ln{2}

k = \frac{\ln{2}}{36}

k = 0.019.

For Country B, the growth rate is of 1.9% per year.

More can be learned about exponential functions at brainly.com/question/25537936

#SPJ1

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