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2 years ago

An exponential function has a growth factor or 3.76. What is the percentage growth rate?

Mathematics

1 answer:

olganol [36]2 years ago

7 0

The exponential function with a growth factor has a rate greater than 1

The percentage growth rate is 276%

<h3>How to determine the percentage growth rate?</h3>

The growth factor (b) is given as:

b = 3.76

The growth factor (b) is greater than 1.

So, the percentage growth rate (r) is calculated as:

r = b - 1

Substitute known values

r = 3.76 - 1

Evaluate the difference

r = 2.76

Express as percentage

r = 276%

Hence, the percentage growth rate is 276%

Read more about exponential functions at:

brainly.com/question/11464095

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Let's re-write the equations in order to get the variables as separated in independent terms as possible \:

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$\frac{xy}{x+y} =1\\xy=x+y\\1=\frac{x+y}{xy} \\1=\frac{1}{y} +\frac{1}{x}$

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$\frac{xz}{x+z} =2\\xz=2\,(x+z)\\\frac{1}{2} =\frac{x+z}{xz} \\\frac{1}{2} =\frac{1}{z} +\frac{1}{x}$

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$\frac{yz}{y+z} =3\\yz=3\,(y+z)\\\frac{1}{3} =\frac{y+z}{yz} \\\frac{1}{3}=\frac{1}{z} +\frac{1}{y}$

Now let's subtract term by term the reduced equation 3 from the reduced equation 1 in order to eliminate the term that contains "y":

$1=\frac{1}{y} +\frac{1}{x} \\-\\\frac{1}{3} =\frac{1}{z} +\frac{1}{y}\\\frac{2}{3} =\frac{1}{x} -\frac{1}{z}$

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