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3 years ago

Is 5 1/25 a rational number

Mathematics

2 answers:

Alla [95]3 years ago

7 0

Answer:

Yes, it is a rational number.

Step-by-step explanation:

Rational numbers are numbers that can be written as a fraction or ratio no matter if it is proper or improper.

Example: Take π for example. Since it goes on forever, it cannot be written a s a fraction or ratio. Therefore it is irrational.

Ending: Therefore, since this can be changed into a fraction, 5 1/5 is rational.

Pavel [41]3 years ago

6 0

5 1/25 is a rational number

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<h3>What is an exponential function?</h3>

The exponential equation for a decaying amount of a substance is given by:

$A(t) = A(0)e^{-rt}$

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

Researching on the internet, the half-life of carbon 14 is of 5,730 years, hence A(5730) = 0.5A(0), which we use to find r.

$A(t) = A(0)e^{-rt}$

$0.5A(0) = A(0)e^{-5730r}$

$e^{-5730r} = 0.5$

$\ln{e^{-5730r}} = \ln{0.5}$

$5730r = -\ln{0.5}$

$r = -\frac{\ln{0.5}}{5730}$

$r = 0.00012096809$

Hence, the equation is:

$A(t) = A(0)e^{-0.00012096809t}$

The wood chips were found to contain 80% of the atmospheric carbon-14, hence we have to find t for which A(t) = 0.8A(0).

$A(t) = A(0)e^{-0.00012096809t}$

$0.8A(0) = A(0)e^{-0.00012096809t}$

$e^{-0.00012096809t} = 0.8$

$\ln{e^{-0.00012096809t}} = \ln{0.8}$

$-0.00012096809t = \ln{0.8}$

$t = -\frac{\ln{0.8}}{0.00012096809}$

$t = 1845$

The Tequesta settlement is 1845 years old.

You can learn more about exponential functions at brainly.com/question/25537936

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