Mathematics, 27.09.2019 05:50 abdominguez7307

Country a has a growth rate of 4.6% per year. the population is currently 5 comma 333,000, and the land area of country a is 27,000,000,000 square yards. assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land? this will happen in nothing years.

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Answer from: blognero

After $t = 189.66\ years$

Step-by-step explanation:

There will be one person per square yard when the number of people is equal to the number of square yards of the country.

In other words, we need to know when the population of the country will be 27,000,000,000.

We know that the population grows exponentially, so we use the exponential growth formula:

P = p_0(1+r)^t

Where:

P is the population as a function of time

p_0 is the initial population

r is the annual growth rate

t is time in year.

The information we have allows us to conclude that:

$r= 4.6\%= 0.046$

p_0 = 5,333,000

So the exponential growth equation is:

P = 5,333,000(1+0.046)^t

We want to know when P = 27, 000,000,000.

So:

27,000,000,000= 5,333,000(1+0.046)^t

Now we solve for t.

$\frac{27,000,000,000}{5,333,000} = (1+0.046)^t$

$log(\frac{27,000,000,000}{5,333,000}) = tlog(1+0.046)$

$t= \frac{log(\frac{27,000,000,000}{5,333,000})}{log(1+0.046)}\\\\\\t = 189.66\ years$

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step-by-step explanation:

Answer from: Quest

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

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