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rewona [7]
3 years ago
10

The initial population of a town in the year 2010 was 20 000. By 2014, the population had grown exponentially to 32 500 people.

Write an equation to represent the population of the town (P) over time in years (n).
Mathematics
1 answer:
stiv31 [10]3 years ago
3 0

Answer:

  P = 20000×1.625^(n/4)

Step-by-step explanation:

An exponential equation can be written using the given data:

  value = (initial value)×(growth factor in period)^(n/(period))

Here, the growth is by a factor of 32500/20000 = 1.625, and the period is 4 years. Then your exponential equation is ...

  P = 20000×1.625^(n/4)

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Answer:

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Now we can apply natural logs on both sides;

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And then the value of t would be:

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Step-by-step explanation:

For this case since we know that the interest is compounded continuously, then we can use the following formula:

A =P e^{rt}

Where A is the future value, P the present value , r the rate of interest in fraction and t the number of years.

For this case we know that P = 100000 and r =0.12 we want to triplicate this amount and that means A= 300000 and we want to find the value for t.

300000= 100000 e^{0.12 t}

We divide both sides by 100000 and we got:

3 = e^{0.12 t}

Now we can apply natural logs on both sides;

ln(3) = 0.12 t

And then the value of t would be:

t = \frac{ln(3)}{0.12}= 9.16 years

And rounded to the nearest tenth would be 9.2 years.

5 0
3 years ago
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Building and solving an inequality, it is found that at a volume of sales of $11,875 he will start to earn more from the commission  based compensation.

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At a volume of sales of $11,875 he will start to earn more from the commission  based compensation.

A similar problem is given at brainly.com/question/17248342

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