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Svetach [21]
3 years ago
12

WILL GIVE BRANLIEST PLS PLS COME LOOK!!!! PRETTY PLS WITH SPRINKLES ON TOP!!!

Mathematics
2 answers:
Elena-2011 [213]3 years ago
5 0
The answer is a on the question
anzhelika [568]3 years ago
4 0

Answer: A

Step-by-step explanation:

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The half life of a radioactive substance is the time it takes for a quantity of the substance to decay to half of the initial am
Veronika [31]

Using an exponential function, it is found that:

a) N(t) = 75(0.5)^{\frac{t}{3.8}}

b) 37.5 grams of the gas remains after 3.8 days.

c) The amount remaining will be of 10 grams after approximately 11 days.

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

A decaying exponential function is modeled by:

A(t) = A(0)(1 - r)^t

In which:

  • A(0) is the initial value.
  • r is the decay rate, as a decimal.

Item a:

We start with 75 grams, and then work with a half-life of 3.8 days, hence the amount after t daus is given by:

N(t) = 75(0.5)^{\frac{t}{3.8}}

Item b:

This is N when t = 3.8, hence:

N(t) = 75(0.5)^{\frac{3.8}{3.8}} = 37.5

37.5 grams of the gas remains after 3.8 days.

Item c:

This is t for which N(t) = 10, hence:

N(t) = 75(0.5)^{\frac{t}{3.8}}

10 = 75(0.5)^{\frac{t}{3.8}}

(0.5)^{\frac{t}{3.8}} = \frac{10}{75}

\log{(0.5)^{\frac{t}{3.8}}} = \log{\frac{10}{75}}

\frac{t}{3.8}\log{0.5} = \log{\frac{10}{75}}

t = 3.8\frac{\log{\frac{10}{75}}}{\log{0.5}}

t \approx 11

The amount remaining will be of 10 grams after approximately 11 days.

More can be learned about exponential functions at brainly.com/question/25537936

4 0
2 years ago
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