The population of a country was 76 million in 1998 and the continuous exponential growt
rate was estimated at per year. Assuming that the population of the country
continues to follow an exponential growth model, find the projected population in 2009.
Round your answer to 1 decimal place.
The approximate population in 2009 is million people

Question

The population of a country was 76 million in 1998 and the continuous exponential growt
rate was estimated at

per year. Assuming that the population of the country
continues to follow an exponential growth model, find the projected population in 2009.
Round your answer to 1 decimal place.
The approximate population in 2009 is million people

UpStudy AI · Accepted Answer

To find the projected population in 2009, we can use the formula for exponential growth:

$$ P(t) = P_0 \times e^{rt} $$

where:
- $$ P(t) $$ is the population at time $$ t $$,
- $$ P_0 $$ is the initial population,
- $$ r $$ is the continuous exponential growth rate,
- $$ t $$ is the time in years.

Given:
- Initial population in 1998, $$ P_0 = 76 $$ million,
- Continuous exponential growth rate, $$ r = 3.2\% = 0.032 $$,
- Time period, $$ t = 2009 - 1998 = 11 $$ years.

Substitute the given values into the formula:

$$ P(11) = 76 \times e^{0.032 \times 11} $$

Now, we can calculate the projected population in 2009.
Calculate the value by following steps:
- step0: Calculate:
  $$76e^{0.032\times 11}$$
- step1: Multiply the numbers:
  $$76e^{0.352}$$
- step2: Convert the expressions:
  $$76e^{\frac{44}{125}}$$
- step3: Rewrite the expression:
  $$76\sqrt[125]{e^{44}}$$
The projected population in 2009 is approximately 108.065048 million people. Rounding this to 1 decimal place, the approximate population in 2009 is 108.1 million people.
The projected population in 2009 is approximately 108.1 million people.

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