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Answer 1

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.

What is the exponential function for population growth?

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

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