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2 years ago

Choose the definition for the function.

Mathematics

1 answer:

kotegsom [21]2 years ago

7 0

The definition of the piecewise function in this problem is given by:

y = x + 1, x ≤ 2.

y = x + 1, x > 2.

<h3>What is a piecewise function?</h3>

A piecewise function is a function that has different definitions, depending on the input.

For x until x = 2, we have a <u>linear function with an intercept of 1 and slope of 1</u>, hence the definition is:

y = x + 1, x ≤ 2.

After x = 2, the function is shifted up one unit, hence:

y = x + 1 + 1, x > 2

y = x + 2, x > 2.

Hence option A is correct.

More can be learned about piecewise functions at brainly.com/question/27262465

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B) 100.42 years.

Step-by-step explanation:

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A) Since we know that population increases exponentially, therefore we will use our given information to form an exponential model for population increase and then we will solve for the time by which our population will be double.

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Now let us solve for t using logarithm.

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Therefore, it will take 63.36 years the population to be double.

B) Now we will find the number of years it will take the population to be triple of its size.

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$\frac{7.1 \times 3}{7.1} =(1.011)^{t}$

$3 =(1.011)^{t}$

Now let us solve for t using logarithm.

$ln(3) =ln (1.011)^{t}$

$ln(3) =t \cdot ln(1.011)$

$1.0986122886681097 =t \cdot 0.0109399400383344$

$t=\frac{1.0986122886681097}{0.0109399400383344}$

$t=100.4221490079915311298\approx 100.42$

Therefore, it will take 100.42 years the population to triple of its size.

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