Would You RATHER...

Mathematics

1 answer:

nekit [7.7K]4 years ago

4 0

Question really depends on the persons mindset wether he/she likes to be rich or a middle person.

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Researchers are monitoring two different radioactive substances. They have 300 grams of substance A which decays at a rate of 0.

Inessa [10]

To model this situation we are going to use the exponential decay function: $f(t)=a(1-b)^t$
where
$f(t)$ is the final amount remaining after $t$ years of decay
$a$ is the initial amount
$b$ is the decay rate in decimal form
$t$ is the time in years

For substance A:
Since we have 300 grams of the substance, $a=300$ . To convert the decay rate to decimal form, we are going to divide the rate by 100%:
$r= \frac{0.15}{100} =0.0015$ . Replacing the values in our function:
$f(t)=a(1-b)^t$
$f(t)=300(1-0.0015)^t$
$f(t)=300(0.9985)^t$ equation (1)

For substance B:
Since we have 500 grams of the substance, $a=500$ . To convert the decay rate to decimal form, we are going to divide the rate by 100%:
$r= \frac{0.37}{100} =0.0037$ . Replacing the values in our function:
$f(t)=a(1-b)^t$
$f(t)=500(1-0.0037)^t$
$f(t)=500(0.9963)^t$ equation (2)

Since they are trying to determine how many years it will be before the substances have an equal mass $M$ , we can replace $f(t)$ with $M$ in both equations:
$M=300(0.9985)^t$ equation (1)
$M=500(0.9963)^t$ equation (2)

We can conclude that the system of equations that can be used to determine how long it will be before the substances have an equal mass, $M$ , is:
$\left \{ {{M=300(0.9985)^t} \atop {M=500(0.9963)^t}} \right.$

Solving the system, we can show that it will take approximately 231.59 years for that to happen.

5 0

3 years ago

Read 2 more answers

What is the total amount paid for a bill of $83.97 with a gratuity of 20%? (Round to the nearest cent.)

ra1l [238]

Answer:

Tip Amount: $ 17

Tip Each Person: $ 17

Bill Each Person: $ 84

Total (Bill + Tip): $ 101

Total Each Person: $ 101

Step-by-step explanation: