Math  /  Data & Statistics

Questionthe interest earned at account's maturity (in 18 years from opening).
7. Currently, the density of Earth's human population DD is about 65 people per square kilometre, or about 1 person per 15,384 square metres. The current population growth rate pp is about 1 percent per year (This roughly corresponds to every family having on average three children.). Find the population density expected in one thousand years from now if the growth rate does not change.

Studdy Solution

STEP 1

1. The current population density D D is 65 people per square kilometer.
2. The annual population growth rate p p is 1% per year.
3. The growth rate remains constant over the next 1000 years.
4. Population growth follows an exponential model.

STEP 2

1. Understand the exponential growth formula.
2. Calculate the population density after 1000 years using the growth formula.

STEP 3

Understand the exponential growth formula. The formula for exponential growth is:
D(t)=D0×(1+p)t D(t) = D_0 \times (1 + p)^t
where: - D(t) D(t) is the population density at time t t , - D0 D_0 is the initial population density, - p p is the growth rate (expressed as a decimal), - t t is the time in years.

STEP 4

Substitute the given values into the exponential growth formula. Here, D0=65 D_0 = 65 , p=0.01 p = 0.01 , and t=1000 t = 1000 .
D(1000)=65×(1+0.01)1000 D(1000) = 65 \times (1 + 0.01)^{1000}

STEP 5

Calculate (1+0.01)1000 (1 + 0.01)^{1000} .
(1.01)1000 (1.01)^{1000}

STEP 6

Using a calculator, compute (1.01)1000 (1.01)^{1000} .
(1.01)100020,959 (1.01)^{1000} \approx 20,959

STEP 7

Multiply the initial density by the growth factor:
D(1000)=65×20,959 D(1000) = 65 \times 20,959
D(1000)1,362,335 D(1000) \approx 1,362,335
The expected population density in one thousand years is approximately:
1,362,335 people per square kilometer \boxed{1,362,335} \text{ people per square kilometer}

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